L7 Constructions 7.1 Construction Introduction Per Date
|
|
- Jeffrey Gilbert
- 6 years ago
- Views:
Transcription
1 7.1 Construction Introduction Per Date In pairs, discuss the meanings of the following vocabulary terms. The first two you should attempt to recall from memory, and for the rest you should try to agree on a working definition suggested by the names of each term. You may use words, drawings, and contextual clues to support your definitions. Once you have developed your working definition with evidence, carefully sketch a visual of the vocabulary term. Try to be as exact as possible. Vocabulary Term Definition with Evidence Parallel Lines asic Construction Perpendicular Lines Midpoint of a Line Segment (#VOC) Perpendicular isector (#VOC) ngle isector (#VOC) Reflection: Was it difficult to be accurate with your sketches? What did you use to ensure increased accuracy? What could you use to ensure increased accuracy? Page 1
2 7.2 Grandma s Hallways Per Date It s time to begin actually building Grandma s house. We re at the point where we need to lay out on the floor the location for the walls. Right now the carpenters are laying out the location for the central hallway and the short hallway opposite its midpoint that leads to the bathroom (as shown on Grandma s house plan). The head carpenter is in charge of this critical step and he s already laid out one wall of the long hallway (see the solid line in the inset below.) ut now he must designate the critical locations for the opposite wall and the connecting short hallway (dotted lines in the inset). elow is a copy of the work order received by the head carpenter from Grandma s Foreman to complete this critical task. Your job is to explain the geometric constructions necessary to completing each task. We must do this to determine what we need to learn to properly lay out Grandma s walls. WORK ORDER #1 1. Goal: Create a short hallway perpendicular to the long hallway, located in such a manner that the line running down the middle of the short hallway bisects the initial wall. Specifications: wall is laid out as indicated by the solid line in the sketch below. Lay out a hallway that will extend perpendicular and opposite the middle of the wall. Note: you can arbitrarily choose the widths of the halls at this point. 2. Goal: Finish the long hallway that uses the original wall as a side. Specifications: Lay out a wall that runs parallel to the original wall (horizontal dotted lines) and perpendicular to the other hallway created. 1. efore proceeding to a step-by-step process for completing this task, explore with a partner how to accurately create this drawing using only patty paper, compass, and straightedge, given one side of the primary hallway as indicated below. You can assume the line below represents the solid line in the inset above. nd that its length is the same as that of the entire main hallway. Note: a straightedge is not a ruler used to measure lengths. Page 2
3 7.2 Grandma s Hallways Per Date We will now investigate what pieces of this puzzle we can achieve using various tools. 2. Using only patty paper and a straightedge, explore how to perform the following constructions. Determine a way to find the midpoint of this line segment. (Remember, you have a straightedge, but not a ruler.) Determine how to draw a perpendicular line to through point C. C Determine how to draw a line through point C that is parallel to. C Page 3
4 7.2 Grandma s Hallways Per Date Determine how to draw a perpendicular bisector of. Reflections: I. What construction(s) were easy to accomplish with patty paper and a straightedge? Why? II. What construction(s) were difficult to accomplish with patty paper and a straightedge? Why? III. What tools might make these constructions easier to complete? IV. If you were the Head Carpenter, would patty paper and a straightedge be useful in laying out the lines on Grandma s floor? Why or why not? Page 4
5 7.2 Grandma s Hallways Per Date 3. We are now going to determine how to find the midpoint and the perpendicular bisector using only a compass and straightedge. Explore with a partner how you might locate the perpendicular bisector with only these two tools. Can you discover a method to construct a perpendicular line through a specific point (not on the line)? What about if that point is on the line? Try to draw some examples of both constructions. Page 5
6 7.2 Grandma s Hallways Per Date Here is a sketch that suggests a method for constructing the perpendicular bisector using only a compass and a straightedge. Were your ideas close? Note: in this sketch we ve used the length of the line segment KLas our radius. It turns out that you can actually use any radius greater than half the length of the segment, and you don t need to draw the entire circles, just their intersects.!### " Thus, since every point on the perpendicular bisector MN simply corresponds to a different choice of the radius used, this implies that every point on the perpendicular bisector of line segment KL is equidistant from the endpoints K and L. This is the Perpendicular isector Theorem, which we prove in L10 Perpendicular Lines and Triangles. On the next page we show how to construct perpendicular lines that pass through a given point that is located either on or off the line. Time permitting, see if you can discover how to do these on your own, without looking at the next page first. Page 6
7 7.2 Grandma s Hallways Per Date Constructing a Perpendicular Line through a point not on the line. Constructing a Perpendicular Line through a point on the line Page 7
8 7.2 Grandma s Hallways Per Date 4. Complete the hallway markings using the compass and straightedge techniques you ve learned. Follow the Hints below. athroom *Hints: Main Hallway Wall i. First draw the center of the side hallway by drawing the perpendicular bisector that passes through the midpoint of the main hallway. ii. iii. iv. Choose a width, using your compass, which is half the width you would like to use for your hallways and mark two points on the main hallway, equidistant from the midpoint of the main hallway. This represents the width of the short hallway. Draw one side of the short hallway by creating the line perpendicular to the main hallway and passing through one of the points you just located. Draw the other side of the short hallway the same way. v. Draw the other wall of the main hallway using the same width and perpendicular lines. Page 8
9 7.2 Grandma s Hallways Per Date Grandma s Hallway Constructions Rubric (circle box you feel you deserve for each category) Line Quality 8 Clear, consistent lines meeting all cross points Neatness 8 No unnecessary or incorrect marks ccuracy of ngle Measures 12 Perfect angle measurements 6 few wavy lines, line wavers off cross points slightly 6 One or two unnecessary or incorrect marks 9 One or two angles with 1-2 measurement errors 4 Inconsistent lines, lines are wavy 4 Three or four unnecessary or incorrect marks 6 Three or four angles with 1-2 measurement errors 2 Lines are not straight, did not use a ruler or straight edge 2 More than four unnecessary or incorrect marks 3 More than four angles with 1-2 measurement errors Student Comments to Teacher: Grandma s Hallway Constructions Rubric (teacher-graded rubric) Line Quality 8 Clear, consistent lines meeting all cross points Neatness 8 No unnecessary or incorrect marks ccuracy of ngle Measures 12 Perfect angle measurements 6 few wavy lines, line wavers off cross points slightly 6 One or two unnecessary or incorrect marks 9 One or two angles with 1-2 measurement errors 4 Inconsistent lines, lines are wavy 4 Three or four unnecessary or incorrect marks 6 Three or four angles with 1-2 measurement errors 2 Lines are not straight, did not use a ruler or straight edge 2 More than four unnecessary or incorrect marks 3 More than four angles with 1-2 measurement errors Teacher Comments to Student: Page 9
10 7.3 Construction Homework Per Date Practice: For each segment, construct a perpendicular line through the given point using only a compass and straightedge. Leave your tick marks to show your work. 1) 2) 3) C 4) Using only a compass and straightedge, construct 2 different size rectangles in the space below. Page 10
11 7.4 Grandma s Hallway Continued Per Date uilding houses always seems rather simple to young apprentices; after all, it mostly consists of measuring and cutting wood, and pounding nails. fter only a few days on the job an apprentice often thinks s/he can do the work as well as anyone. In the middle of laying out Grandma s hallways the Head Carpenter took his lunch break. He had only located the midpoint of the first wall when he took the break. Scotty, a young apprentice on the job for less than a week decided to stay behind and impress the boss with his ability to continue laying out the main hallway. His results are shown below (dotted line that appears to be parallel to the solid line). Scotty doesn t have any tools, being only an apprentice, and the Head Carpenter took all the tools except his protractor. There is also another faint dotted line on the floor that was left by an abandoned layout. How can Scotty use only the protractor to check the accuracy of his work? Hint: recall what you ve learned about parallel lines cut by a transversal. Reflection: How did Scotty do? Explain what information is important in this situation. Given two intersecting lines, say l and m, what could you check to see if the lines are parallel? Note: In reality a Carpenter will simply measure the desired width of the hallway at either end and connect the dots. Nevertheless, the fact presented herein, and many others as well, are well known and often used by the best master builders if not the apprentices. Page 11
12 7.5 Grandma s Garden Plot Per Date Now that Grandma s hallway is under construction, she has more time to work in her garden. Grandma would like to grow some rose bushes and hibiscus plants in an obtuse corner of her lot. WORK ORDER #2 1. Goal: Design the layout for a flower garden with equal area for roses and hibiscus flowers. Specifications: Divide the non-perpendicular corner of the lot into two congruent sections for roses and hibiscus flowers by drawing an angle bisector as indicated in the sketch. This is a blown up version of the flower garden located in the lower left-hand corner of Granma s Plot Plan. 2. Goal: Enclose the areas for the Roses and Hibiscus in triangular plots that have equal area. Specifications: Pick a point on the dotted line that represents a point on your desired boundary for your growing plot. Draw equal length lines from this point to the two solid rays. Explore with a partner how you might bisect using only a compass and straightedge. Hint: think about how you used the compass and straightedge in earlier constructions. Page 12
13 7.5 Grandma s Garden Plot Per Date efore proceeding to using a compass, try answering the following using only patty paper and a straightedge: 1. Determine a way to copy C. C Determine a way to bisect C. C Reflection: i. Which construction was easiest to accomplish with patty paper and a straightedge? Why? ii. If you were asked to map out Grandma s Garden Plot in a real situation, would patty paper and a straightedge be useful? Why or why not? Now let s try it with a compass and straightedge: Page 13
14 7.5 Grandma s Garden Plot Per Date 2. Determine a way to copy C using only a straightedge and compass. Hint: think about your earlier compass and straightedge constructions. compass can be used to capture distances and locate points, and a straightedge can be used to connect two points. The base of the angle is provided to the right, along with a single arbitrarily chosen point. C Determine a way to bisect C using only a straightedge and compass. Hint: think about your earlier compass and straightedge constructions. C Page 14
15 7.5 Grandma s Garden Plot Per Date Practice: efore you complete your task to help Grandma and her Garden Plot, practice copying and bisecting angles. 3. isect the following angles on the left, then copy the original angle to the right. C D E F G H I Page 15
16 7.5 Grandma s Garden Plot Per Date 4. isect the following angles and the left, then copy the bisected angle on the right. J K L M O N 5. Kimo is practicing to help Grandma with her Garden Plot. He believes he has correctly copied and bisected the angle on the left below, with his results to the right. How did Kimo do? Use a straightedge and compass to check Kimo s work. Page 16
17 7.5 Grandma s Garden Plot Per Date Here is the obtuse corner in Grandma s property lot. Use the information that you are learning (ahead and after this page) to complete Work Order #2. Page 17
18 7.6 Grandma s Garden Plot Homework Per Date Homework: Complete the following geometric construction tasks with a compass and straightedge. Check your work with a protractor. Remember to leave your marks to demonstrate your accurate construction actions. 1. isect C with a line segment. Name this line segment D. Extend line segment D 4 inches from point (use a ruler for this). 2. Draw a perpendicular bisector from D towards the top-left of the paper. Extend this segment 2 inches from D. Name this line segment EF with point E on D. 3. Draw a parallel line segment to D, named GH and passing through point F. This drawing will be graded for accuracy with respect to following directions and measurements. C Page 18
19 7.7 Parallel Lines Proofs Per Date Let s now prove some of our previous conjectures. 1. While construction ensues on Grandma s house, her grandson Koa teaches her about what he is learning in class this year. He shows Grandma this image and makes the following conclusion: If j k, then. Grandma looks over the image and adds another line. She asks Koa, ased on your conclusions, does this mean that 2 is congruent to 3? Koa looks carefully at the image and responds. What should Koa s response to Grandma be? What evidence could he have used to support his conclusion? Page 19
20 7.7 Parallel Lines Proofs Per Date Explore with a partner the following, using patty paper and/or rigid transformations: Which pairs of angles in the above diagram do you need to know are congruent before you can!##"!##" conclude that the lines and DE are parallel? Each answer should be a single pair of angles. Why do you think each single pair implies the desired result? e as specific as possible. The following theorem is the Converse to the Parallel Postulate. Rather than prove this theorem at this time, which is essentially based on the fact that the three angles in a triangle sum to180, we will assume it to be true. Converse of the Parallel Postulate (#THM): If two lines are cut by a transversal such that the interior angles sum to 180 then the two lines are parallel. This is equivalent to saying that if two lines are not parallel then the interior angles will not sum to 180, which is what Koa could have replied to his Grandma in the previous problem. Note: This postulate is very useful when trying to prove two lines are parallel. Page 20
21 7.7 Parallel Lines Proofs Per Date efore proceeding to the next proofs, identify each pair of angles in the diagram below that have the property: if the pair of angles are congruent then the two lines and DE must be parallel. Which transformations and other facts seem to justify your conjectures? We will prove these conjectures below, although we will use non-transformation results to do so. Pairs of ngles that you believe must be Congruent Transformation or Facts Used to Justify your Result Page 21
22 7.7 Parallel Lines Proofs Per Date 2. Given: C DE (#THM Corresponding ngles Converse) suur suur Prove: DF. Statement Reason Page 22
23 7.7 Parallel Lines Proofs Per Date C G D H E F 3. Given: GE DE (#THM lternate Interior ngles Converse) suur suur Prove: DF. Statement Reason Page 23
24 7.7 Parallel Lines Proofs Per Date C G D H E F 4. Given: C HEF (#THM lternate Exterior ngles Converse)!##" Prove:!##" DF. Statement Reason Page 24
25 7.8 Parallel Lines Proofs Homework Per Date C G D H E F!##" Given:!##" DF Prove: C + DEH = 180. Statement Reason Page 25
Step 2: Extend the compass from the chosen endpoint so that the width of the compass is more than half the distance between the two points.
Student Name: Teacher: Date: District: Miami-Dade County Public Schools Test: 9_12 Mathematics Geometry Exam 1 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the given
More information6.1 Justifying Constructions
Name lass ate 6.1 Justifying onstructions Essential Question: How can you be sure that the result of a construction is valid? Resource Locker Explore 1 Using a Reflective evice to onstruct a erpendicular
More informationAssignment. Visiting Washington, D.C. Transversals and Parallel Lines
Assignment Assignment for Lesson.1 Name Date Visiting Washington, D.C. Transversals and Parallel Lines Do not use a protractor in this assignment. Rely only on the measurements given in each problem. 1.
More informationGeometric Constructions
Geometric onstructions (1) opying a segment (a) Using your compass, place the pointer at Point and extend it until reaches Point. Your compass now has the measure of. (b) Place your pointer at, and then
More informationUsing Geometry. 9.1 Earth Measure. 9.2 Angles and More Angles. 9.3 Special Angles. Introduction to Geometry and Geometric Constructions...
Using Geometry Recognize these tools? The one on the right is a protractor, which has been used since ancient times to measure angles. The one on the left is a compass, used to create arcs and circles.
More informationS. Stirling Page 1 of 14
3.1 Duplicating Segments and ngles [and riangles] hese notes replace pages 144 146 in the book. You can read these pages for extra clarifications. Instructions for making geometric figures: You can sketch
More informationFind the coordinates of the midpoint of a segment having the given endpoints.
G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to
More informationObjective: Use a compass and straight edge to construct congruent segments and angles.
CONSTRUCTIONS Objective: Use a compass and straight edge to construct congruent segments and angles. Introduction to Constructions Constructions: The drawing of various shapes using only a pair of compasses
More informationObjective: Use a compass and straight edge to construct congruent segments and angles.
CONSTRUCTIONS Objective: Use a compass and straight edge to construct congruent segments and angles. Oct 1 8:33 AM Oct 2 7:42 AM 1 Introduction to Constructions Constructions: The drawing of various shapes
More informationSec Geometry - Constructions
Sec 2.2 - Geometry - Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB. A B C **Using a ruler measure the two lengths to make sure they have
More informationConstructions. Unit 9 Lesson 7
Constructions Unit 9 Lesson 7 CONSTRUCTIONS Students will be able to: Understand the meanings of Constructions Key Vocabulary: Constructions Tools of Constructions Basic geometric constructions CONSTRUCTIONS
More informationMath 3 Geogebra Discovery - Equidistance Decemeber 5, 2014
Math 3 Geogebra Discovery - Equidistance Decemeber 5, 2014 Today you and your partner are going to explore two theorems: The Equidistance Theorem and the Perpendicular Bisector Characterization Theorem.
More informationCONSTRUCTION #1: Segment Copy
CONSTRUCTION #1: Segment Copy Objective: Given a line segment, construct a line segment congruent to the given one. Procedure: After doing this Your work should look like this Start with a line segment
More informationCh. 3 Parallel and Perpendicular Lines
Ch. 3 Parallel and Perpendicular Lines Section 3.1 Lines and Angles 1. I CAN identify relationships between figures in space. 2. I CAN identify angles formed by two lines and a transversal. Key Vocabulary:
More informationLesson 3.1 Duplicating Segments and Angles
Lesson 3.1 Duplicating Segments and ngles Name eriod Date In Exercises 1 3, use the segments and angles below. omplete the constructions on a separate piece of paper. S 1. Using only a compass and straightedge,
More informationGeometry SOL G.4 Constructions Name Date Block. Constructions
Geometry SOL G.4 Constructions Mrs. Grieser Name Date Block Constructions Grab your compass and straight edge - it s time to learn about constructions!! On the following pages you will find instructions
More informationThe Basics: Geometric Structure
Trinity University Digital Commons @ Trinity Understanding by Design: Complete Collection Understanding by Design Summer 6-2015 The Basics: Geometric Structure Danielle Kendrick Trinity University Follow
More information6.1 Warm Up The diagram includes a pair of congruent triangles. Use the congruent triangles to find the value of x in the diagram.
6.1 Warm Up The diagram includes a pair of congruent triangles. Use the congruent triangles to find the value of x in the diagram. 1. 2. Write a proof. 3. Given: P is the midpoint of MN and TQ. Prove:
More informationChallenges from Ancient Greece
Challenges from ncient Greece Mathematical goals Make formal geometric constructions with a variety of tools and methods. Use congruent triangles to justify geometric constructions. Common Core State Standards
More informationLesson 9.1 Assignment
Lesson 9.1 Assignment Name Date Earth Measure Introduction to Geometry and Geometric Constructions Use a compass and a straightedge to complete Questions 1 and 2. 1. Construct a flower with 12 petals by
More informationUnit 6 Guided Notes. Task: To discover the relationship between the length of the mid-segment and the length of the third side of the triangle.
Unit 6 Guided Notes Geometry Name: Period: Task: To discover the relationship between the length of the mid-segment and the length of the third side of the triangle. Materials: This paper, compass, ruler
More informationName Period Date. GEOMETRY AND MEASURESUREMENT Student Pages for Packet 6: Drawings and Constructions
Name Period Date GEOMETRY AND MEASURESUREMENT Student Pages for Packet 6: Drawings and Constructions GEO6.1 Geometric Drawings Review geometric notation and vocabulary. Use a compass and a ruler to make
More informationConstructing Angle Bisectors and Parallel Lines
Name: Date: Period: Constructing Angle Bisectors and Parallel Lines TASK A: 1) Complete the following steps below. a. Draw a circle centered on point P. b. Mark any two points on the circle that are not
More informationTopic 1 Chapter 3: Constructions Greek philosopher Plato Euclid(Elements)
Topic 1 Chapter 3: Constructions Greek philosopher Plato Euclid(Elements) 1. Duplicating (copying) a segment 2. Duplicating (copying) an angle 3. Constructing the bisector of a segment (bisecting a segment)
More informationName: Date: Chapter 2 Quiz Geometry. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Date: Chapter 2 Quiz Geometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the value of x? Identify the missing justifications.,, and.
More informationGeometry Vocabulary Book
Geometry Vocabulary Book Units 2-4 Page 1 Unit 2 General Geometry Point Characteristics: Line Characteristics: Plane Characteristics: RELATED POSTULATES: Through any two points there exists exactly one
More informationCircles Assignment Answer the following questions.
Answer the following questions. 1. Define constructions. 2. What are the basic tools that are used to draw geometric constructions? 3. What is the use of constructions? 4. What is Compass? 5. What is Straight
More information1-2 Measuring and Constructing Segments. Holt Geometry
1-2 Measuring and Constructing Segments Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Vocabulary coordinate midpoint distance bisect length segment bisector
More information16.1 Segment Length and Midpoints
Name lass ate 16.1 Segment Length and Midpoints Essential Question: How do you draw a segment and measure its length? Explore Exploring asic Geometric Terms In geometry, some of the names of figures and
More informationStretch lesson: Constructions
29 Stretch lesson: onstructions Stretch objectives efore you start this chapter, mark how confident you feel about each of the statements below: I can construct the perpendicular bisector of a given line.
More informationWorksheet 10 Memorandum: Construction of Geometric Figures. Grade 9 Mathematics
Worksheet 10 Memorandum: Construction of Geometric Figures Grade 9 Mathematics For each of the answers below, we give the steps to complete the task given. We ve used the following resources if you would
More information9.3 Properties of Chords
9.3. Properties of Chords www.ck12.org 9.3 Properties of Chords Learning Objectives Find the lengths of chords in a circle. Discover properties of chords and arcs. Review Queue 1. Draw a chord in a circle.
More informationParallel and Perpendicular Lines
Practice A Parallel and Perpendicular Lines 1. Measure the formed by the transversal and the parallel lines. Which seem to be congruent? In the figure, line r line s. Find the measure of each angle. 2.
More informationMeasuring and Drawing Angles and Triangles
NME DTE Measuring and Drawing ngles and Triangles Measuring an angle 30 arm origin base line 0 180 0 If the arms are too short to reach the protractor scale, lengthen them. Step 1: lace the origin of the
More informationIndicate whether the statement is true or false.
MATH 121 SPRING 2017 - PRACTICE FINAL EXAM Indicate whether the statement is true or false. 1. Given that point P is the midpoint of both and, it follows that. 2. If, then. 3. In a circle (or congruent
More information(Geometry) Academic Standard: TLW use appropriate tools to perform basic geometric constructions.
Seventh Grade Mathematics Assessments page 1 (Geometry) Academic Standard: TLW use appropriate tools to perform basic geometric constructions. A. TLW use tools to draw squares, rectangles, triangles and
More informationGeometry Unit 3 Note Sheets Date Name of Lesson. Slopes of Lines. Partitioning a Segment. Equations of Lines. Quiz
Date Name of Lesson Slopes of Lines Partitioning a Segment Equations of Lines Quiz Introduction to Parallel and Perpendicular Lines Slopes and Parallel Lines Slopes and Perpendicular Lines Perpendicular
More informationParallel and Perpendicular Lines on the Coordinate Plane
Did You Find a Parking Space? Parallel and Perpendicular Lines on the Coordinate Plane 1.5 Learning Goals Key Term In this lesson, you will: Determine whether lines are parallel. Identify and write the
More informationThe 7* Basic Constructions Guided Notes
Name: The 7* asic Constructions Guided Notes Included: 1. Given an segment, construct a 2 nd segment congruent to the original. (ctually not included!) 2. Given an angle, construct a 2 nd angle congruent
More informationGeometry by Jurgensen, Brown and Jurgensen Postulates and Theorems from Chapter 1
Postulates and Theorems from Chapter 1 Postulate 1: The Ruler Postulate 1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1. 2. Once
More informationMeasuring and Constructing Angles Going Deeper
Name Class 1-3 Date Measuring and Constructing ngles Going Deeper Essential question: What tools and methods can you use to copy an angle and bisect an angle? n angle is a figure formed by two rays with
More informationAxiom A-1: To every angle there corresponds a unique, real number, 0 < < 180.
Axiom A-1: To every angle there corresponds a unique, real number, 0 < < 180. We denote the measure of ABC by m ABC. (Temporary Definition): A point D lies in the interior of ABC iff there exists a segment
More informationUNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 3: Constructing Polygons Instruction
rerequisite Skills This lesson requires the use of the following skills: using a compass copying and bisecting line segments constructing perpendicular lines constructing circles of a given radius Introduction
More informationUNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 2: Constructing Lines, Segments, and Angles Instruction
Prerequisite Skills This lesson requires the use of the following skills: using a compass understanding the geometry terms line, segment, ray, and angle Introduction Two basic instruments used in geometry
More informationWhat You ll Learn. Why It s Important
Many artists use geometric concepts in their work. Think about what you have learned in geometry. How do these examples of First Nations art and architecture show geometry ideas? What You ll Learn Identify
More informationPre-Test. Name Date. 1. Can skew lines be coplanar? Explain.
Pre-Test Name Date 1. Can skew lines be coplanar? Explain. 2. Point D is at the center of a circle. Points A, B, and C are on the same arc of the circle. What can you say about the lengths of AD, BD, and
More informationUnit 1 Foundations of Geometry: Vocabulary, Reasoning and Tools
Number of Days: 34 9/5/17-10/20/17 Unit Goals Stage 1 Unit Description: Using building blocks from Algebra 1, students will use a variety of tools and techniques to construct, understand, and prove geometric
More informationFolding Activity 3. Compass Colored paper Tape or glue stick
Folding Activity 3 Part 1 You re not done until everyone in your group is done! If you finish before someone else, help them finish before starting on the next part. You ll need: Patty paper Ruler Sharpie
More informationGeometer s Skethchpad 8th Grade Guide to Learning Geometry
Geometer s Skethchpad 8th Grade Guide to Learning Geometry This Guide Belongs to: Date: Table of Contents Using Sketchpad - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
More informationGeometry Ch 3 Vertical Angles, Linear Pairs, Perpendicular/Parallel Lines 29 Nov 2017
3.1 Number Operations and Equality Algebraic Postulates of Equality: Reflexive Property: a=a (Any number is equal to itself.) Substitution Property: If a=b, then a can be substituted for b in any expression.
More informationAngles formed by Transversals
Section 3-1: Parallel Lines and Transversals SOL: None Objectives: Identify the relationships between two lines or two planes Name angles formed by a pair of lines and a transversal Vocabulary: Parallel
More informationPerry High School. Geometry: Week 3
Geometry: Week 3 Monday: Labor Day! Tuesday: 1.5 Segments and Angle Bisectors Wednesday: 1.5 - Work Thursday: 1.6 Angle Pair Relationships Friday: 1.6-Work Next Week 1.7, Review, Exam 1 on FRIDAY 1 Tuesday:
More information3. Given the similarity transformation shown below; identify the composition:
Midterm Multiple Choice Practice 1. Based on the construction below, which statement must be true? 1 1) m ABD m CBD 2 2) m ABD m CBD 3) m ABD m ABC 1 4) m CBD m ABD 2 2. Line segment AB is shown in the
More information16. DOK 1, I will succeed." In this conditional statement, the underlined portion is
Geometry Semester 1 REVIEW 1. DOK 1 The point that divides a line segment into two congruent segments. 2. DOK 1 lines have the same slope. 3. DOK 1 If you have two parallel lines and a transversal, then
More informationChapter 11: Constructions and Loci
Chapter 11: Section 11.1a Constructing a Triangle given 3 sides (sss) Leave enough room above the line to complete the shape. Do not rub out your construction lines. They show your method. 1 Section 11.1b
More information1. Construct the perpendicular bisector of a line segment. Or, construct the midpoint of a line segment. 1. Begin with line segment XY.
1. onstruct the perpendicular bisector of a line segment. Or, construct the midpoint of a line segment. 1. egin with line segment. 2. lace the compass at point. djust the compass radius so that it is more
More informationE G 2 3. MATH 1012 Section 8.1 Basic Geometric Terms Bland
MATH 1012 Section 8.1 Basic Geometric Terms Bland Point A point is a location in space. It has no length or width. A point is represented by a dot and is named by writing a capital letter next to the dot.
More informationThe Magic Circle Basic Lesson. Developed by The Alexandria Seaport Foundation
The Magic Circle Basic Lesson Developed by The Alexandria Seaport Foundation The Tools Needed Compass Straightedge Pencil Paper (not graph paper, 8.5 x 11 is fine) Your Brain (the most important tool!)
More informationGeorgia Department of Education Common Core Georgia Performance Standards Framework Analytic Geometry Unit 1
Lunch Lines Mathematical Goals Prove vertical angles are congruent. Understand when a transversal is drawn through parallel lines, special angles relationships occur. Prove when a transversal crosses parallel
More informationMathematical Construction
Mathematical Construction Full illustrated instructions for the two bisectors: Perpendicular bisector Angle bisector Full illustrated instructions for the three triangles: ASA SAS SSS Note: These documents
More informationObjective: Draw kites and squares to clarify their attributes, and define kites and squares based on those attributes.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 19 5 5 Lesson 19 Objective: Draw kites and squares to clarify their attributes, and define kites and Suggested Lesson Structure Fluency Practice Application
More informationTeacher Lesson Pack Lines and Angles. Suitable for Gr. 6-9
Teacher Lesson Pack Lines and Angles Suitable for Gr. 6-9 1 2 Sir Cumference and the Great Knight of Angleland By: Cindy Neuschwander, Charlsebridge Publishing, ISBN: 1570911525 Read the book to the students.
More information1.2 Angle Measures and Angle Bisectors
Name Class Date 1.2 ngle easures and ngle isectors Essential uestion: How is measuring an angle similar to and different from measuring a line segment? G.5. Construct congruent angles, an angle bisector
More informationCCM Unit 10 Angle Relationships
CCM6+7+ Unit 10 Angle Relationships ~ Page 1 CCM6+7+ 2016-17 Unit 10 Angle Relationships Name Teacher Projected Test Date Main Concepts Page(s) Unit 10 Vocabulary 2-3 Measuring Angles with Protractors
More information12 Constructions and Loci
MEP Y9 Practice ook 12 onstructions and Loci 12.1 Recap: ngles and Scale Drawing The concepts in this unit rely heavily on knowledge acquired previously, particularly for angles and scale drawings, so
More informationSession 1 What Is Geometry?
Key Terms for This Session Session 1 What Is Geometry? New in This Session altitude angle bisector concurrent line line segment median midline perpendicular bisector plane point ray Introduction In this
More informationTarget 5.4: Use angle properties in triangles to determine unknown angle measurements 5.4: Parallel Lines and Triangles
Unit 5 Parallel and Perpendicular Lines Target 5.1: Classify and identify angles formed by parallel lines and transversals 5.1 a Parallel and Perpendicular lines 5.1b Parallel Lines and its Angle Relationships
More informationName Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines
Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines Two lines are if they are coplanar and do not intersect. Skew lines. Two
More informationVocabulary slope, parallel, perpendicular, reciprocal, negative reciprocal, horizontal, vertical, rise, run (earlier grades)
Slope Reporting Category Reasoning, Lines, and Transformations Topic Exploring slope, including slopes of parallel and perpendicular lines Primary SOL G.3 The student will use pictorial representations,
More information9.1 and 9.2 Introduction to Circles
Date: Secondary Math 2 Vocabulary 9.1 and 9.2 Introduction to Circles Define the following terms and identify them on the circle: Circle: The set of all points in a plane that are equidistant from a given
More informationProperties of Chords
Properties of Chords Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit www.ck12.org
More information23.2 Angle Bisectors of Triangles
Name lass Date 23.2 ngle isectors of Triangles Essential uestion: How can you use angle bisectors to find the point that is equidistant from all the sides of a triangle? Explore Investigating Distance
More informationSlopes of Lines Notes What is slope?
Slopes of Lines Notes What is slope? Find the slope of each line. 1 Find the slope of each line. Find the slope of the line containing the given points. 6, 2!!"#! 3, 5 4, 2!!"#! 4, 3 Find the slope of
More informationMath 21 Home. Book 8: Angles. Teacher Version Assessments and Answers Included
Math 21 Home Book 8: Angles Teacher Version Assessments and Answers Included Year Overview: Earning and Spending Money Home Travel & Transportation Recreation and Wellness 1. Budget 2. Personal Banking
More informationProperties of Special Parallelograms
LESSON 5.5 You must know a great deal about a subject to know how little is known about it. LEO ROSTEN Properties of Special Parallelograms The legs of the lifting platform shown at right form rhombuses.
More information7th Grade Drawing Geometric Figures
Slide 1 / 53 Slide 2 / 53 7th Grade Drawing Geometric Figures 2015-11-23 www.njctl.org Slide 3 / 53 Topics Table of Contents Determining if a Triangle is Possible Click on a topic to go to that section
More informationInvestigation 1 Going Off on a Tangent
Investigation 1 Going Off on a Tangent a compass, a straightedge In this investigation you will discover the relationship between a tangent line and the radius drawn to the point of tangency. Construct
More informationName. Ms. Nong. Due on: Per: Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0
Name FRIDAY, FEBRUARY 24 Due on: Per: TH Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume
More informationSemester 1 Final Exam Review
Target 1: Vocabulary and notation Semester 1 Final Exam Review Name 1. Find the intersection of MN and LO. 2. 3) Vocabulary: Define the following terms and draw a diagram to match: a) Point b) Line c)
More information6. True or false? Shapes that have no right angles also have no perpendicular segments. Draw some figures to help explain your thinking.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 3 Homework 4 4 5. Use your right angle template as a guide and mark each right angle in the following figure with a small square. (Note that a right angle
More information3.1 Start Thinking. 3.1 Warm Up. 3.1 Cumulative Review Warm Up
3.1 Start Thinking Sketch two perpendicular lines that intersect at point. Plot one point on each line that is not. all these points and. onnect and to make. What type of figure do points,, and make? ould
More information*Unit 1 Constructions and Transformations
*Unit 1 Constructions and Transformations Content Area: Mathematics Course(s): Geometry CP, Geometry Honors Time Period: September Length: 10 blocks Status: Published Transfer Skills Previous coursework:
More informationProject Maths Geometry Notes
The areas that you need to study are: Project Maths Geometry Notes (i) Geometry Terms: (ii) Theorems: (iii) Constructions: (iv) Enlargements: Axiom, theorem, proof, corollary, converse, implies The exam
More informationLocus Locus. Remarks
4 4. The locus of a point is the path traced out by the point moving under given geometrical condition (or conditions). lternatively, the locus is the set of all those points which satisfy the given geometrical
More informationb. Describe how a horizontal translation changes the coordinates of the endpoints.
Pre-Test Name Date. Determine the distance between the points (5, 2) and (2, 6). 2. Mari draws line segment AB on a coordinate plane. The coordinates of A are (, 5). The coordinates of B are (23, 2). She
More informationLesson 10.1 Skills Practice
Lesson 10.1 Skills Practice Location, Location, Location! Line Relationships Vocabulary Write the term or terms from the box that best complete each statement. intersecting lines perpendicular lines parallel
More informationRegents Exam Questions by Topic Page 1 TOOLS OF GEOMETRY: Constructions NAME:
Regents Exam Questions by Topic Page 1 1. 060925ge, P.I. G.G.17 Which illustration shows the correct construction of an angle bisector? [A] 3. 060022a, P.I. G.G.17 Using only a ruler and compass, construct
More information5.1. Perpendiculars and Bisectors. What you should learn
age 1 of 8 5.1 erpendiculars and isectors What you should learn GOL 1 Use properties of perpendicular bisectors. GOL 2 Use properties of angle bisectors to identify equal distances, such as the lengths
More informationObjective: Draw rectangles and rhombuses to clarify their attributes, and define rectangles and rhombuses based on those attributes.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 5 5 Lesson 18 Objective: Draw rectangles and rhombuses to clarify their attributes, and define Suggested Lesson Structure Fluency Practice Application Problem
More informationGeometry Station Activities for Common Core State Standards
Geometry Station Activities for Common Core State Standards WALCH EDUCATION Table of Contents Standards Correlations...................................................... v Introduction..............................................................vii
More information9.1 Properties of Parallelograms
Name lass ate 9.1 Properties of Parallelograms Essential Question: What can you conclude about the sides, angles, and diagonals of a parallelogram? Explore Investigating Parallelograms quadrilateral is
More informationSTRAND H: Angle Geometry
Mathematics SKE, Strand H UNIT H3 onstructions and Loci: Text STRND H: ngle Geometry H3 onstructions and Loci Text ontents Section H3.1 Drawing and Symmetry H3.2 onstructing Triangles and ther Shapes H3.3
More informationUnit 6 Lesson 1 Circle Geometry Properties Project
Unit 6 Lesson 1 Circle Geometry Properties Project Name Part A Look up and define the following vocabulary words. Use an illustration where appropriate. Some of this vocabulary can be found in the glossary
More informationAngle Measure and Plane Figures
Grade 4 Module 4 Angle Measure and Plane Figures OVERVIEW This module introduces points, lines, line segments, rays, and angles, as well as the relationships between them. Students construct, recognize,
More informationTable of Contents. Standards Correlations...v Introduction...vii Materials List... x
Table of Contents Standards Correlations...v Introduction...vii Materials List... x...1...1 Set 2: Classifying Triangles and Angle Theorems... 13 Set 3: Corresponding Parts, Transformations, and Proof...
More informationFoundations for Geometry Review Sheet
Name: Date: Block: Foundations for Geometry Review Sheet 1.1-1.5 Show all work to receive full credit. This is will be collected the day of the test. 1) Draw and define line segment AB: 2) Draw and define
More informationand Transitional Comprehensive Curriculum. Geometry Unit 3: Parallel and Perpendicular Relationships
Geometry Unit 3: Parallel and Perpendicular Relationships Time Frame: Approximately three weeks Unit Description This unit demonstrates the basic role played by Euclid s fifth postulate in geometry. Euclid
More informationLesson 1.7.4: Solving Problems Using Similarity and Congruence Warm-Up 1.7.4
Unit2SolvingProblemsusingSimilarity Lesson 1.7.4: Solving Problems Using Similarity and ongruence Warm-Up 1.7.4 Three buildings border a triangular courtyard as shown in the diagram. walkway runs parallel
More informationWarm-Up Up Exercises. 1. Find the value of x. ANSWER 32
Warm-Up Up Exercises 1. Find the value of x. ANSWER 32 2. Write the converse of the following statement. If it is raining, then Josh needs an umbrella. ANSWER If Josh needs an umbrella, then it is raining.
More informationHow to Design a Geometric Stained Glass Lamp Shade
This technique requires no calculation tables, math, or angle computation. Instead you can use paper & pencil with basic tech drawing skills to design any size or shape spherical lamp with any number of
More information