Properties of Special Parallelograms

Size: px
Start display at page:

Download "Properties of Special Parallelograms"

Transcription

1 Properties of Special Parallelograms Lab Summary: This lab consists of four activities that lead students through the construction of a trapezoid. Students then explore the shapes, making conclusions about the angles, diagonals, and sides of the shapes. Key Words: trapezoid Background Knowledge: Students should be familiar with the basic geometry software commands. This lab does not provided step by step instructions for constructing a trapezoid. Therefore, students should understand that to construct a trapezoid, parallel lines must be constructed first to serve as the bases of a trapezoid. To construct the legs, students then must construct segments connecting the parallel lines. Learning Objectives: Students will identify the basic properties of trapezoids. Materials: Geometry software Suggested procedure: Split students into groups of two or three. Pass out worksheets Assessment: Check the completed worksheets and student constructions.

2 Trapezoids Team members names: File name: Goal: Construct a trapezoid and analyze some of it properties. 1. This lab does not give you step by step instructions. Using your prior Cabri skills, construct a Trapezoid. The guidelines for a trapezoid are given below. A trapezoid has the following properties: It is four sided Two sides are parallel Label the vertices K, L, M, and N An example is shown below: 2. In your own words, explain how you constructed this trapezoid: The parallel sides of the trapezoid are called the bases and the nonparallel sides are called the legs. The angles at the ends of the base are called base angles. 3. What are the base angles and the sides (How many)? What are the leg angles and sides (How many)?

3 Note: If students are not familiar with Cabri, press F1 on the keyboard. A help menu for each tool selected will appear on the bottom of the screen. Now, we will take a look at a special type of trapezoid called an isosceles trapezoid. 1. Construct a circle and label the center of the circle P [Use circle tool] 2. Draw a line P and label line l. [Use the line tool] 3. Label the points E and F that intersect the line and the circle [Use the point tool] 4. Pick a point Q inside the circle, not on P. [Use the point tool] 5. Construct a parallel line m to line l [Use the parallel line tool] 6. Label the intersection of this line and the circle points G and H. [Use the point tool] 7. Now construct segments EF, FG, GH, and HE. 8. Hide lines l and m and the circle. [Use hide and show tool] Measure the sides and angles of the isosceles trapezoid and complete the chart below: Name of Side Length Name of Angle Measurement What observations can you make about the bases, the legs and the base angles? Complete the following properties: The bases of an isosceles trapezoid are always. The legs of an isosceles trapezoid are always. The base angles of an isosceles trapezoid are always.

4 Now, compare and contrast trapezoids to the other quadrilaterals. Is a trapezoid a parallelogram (hint- defining characteristic of a parallelogram)? Why or why not? Is a trapezoid a kite (hint what defines a kite)? Why or why not? Let s reflect! In the space below, draw a rough sketch of each quadrilateral. Rhombus Parallelogram Rectangle Kite Trapezoid Square

5 Note: If students are not familiar with Cabri, press F1 on the keyboard. A help menu for each tool selected will appear on the bottom of the screen Extension: Compare and contrast the different kinds of quadrilaterals. Display your information as a written summary, diagram or chart. Compare these finding to the hands-on experience with quadrilaterals, Lab #1. Complete a final Venn Diagram or tree (similar to a family tree) showing the relationship of the following quadrilaterals: isosceles trapezoid, kite, parallelogram, rectangle, rhombus, square, and trapezoid.

6 Extension: Using Cabri construct a Venn Diagram that shows the relationship of quadrilaterals, parallelograms, rectangles, squares, kites, and trapezoids. An example of a Venn Diagram is shown below.

7 Extension: Using Cabri construct a Venn Diagram that shows the relationship of quadrilaterals, parallelograms, rectangles, squares, kites, trapezoids, and isosceles trapezoids. An example of a Venn Diagram is shown below.

All in the Family. b. Use your paper tracing to compare the side lengths of the parallelogram. What appears to be true? Summarize your findings below.

All in the Family. b. Use your paper tracing to compare the side lengths of the parallelogram. What appears to be true? Summarize your findings below. The quadrilateral family is organized according to the number pairs of sides parallel in a particular quadrilateral. Given a quadrilateral, there are three distinct possibilities: both pairs of opposite

More information

18 Two-Dimensional Shapes

18 Two-Dimensional Shapes 18 Two-Dimensional Shapes CHAPTER Worksheet 1 Identify the shape. Classifying Polygons 1. I have 3 sides and 3 corners. 2. I have 6 sides and 6 corners. Each figure is made from two shapes. Name the shapes.

More information

To Explore the Properties of Parallelogram

To Explore the Properties of Parallelogram Exemplar To Explore the Properties of Parallelogram Objective To explore the properties of parallelogram Dimension Measures, Shape and Space Learning Unit Quadrilaterals Key Stage 3 Materials Required

More information

Geometry. a) Rhombus b) Square c) Trapezium d) Rectangle

Geometry. a) Rhombus b) Square c) Trapezium d) Rectangle Geometry A polygon is a many sided closed shape. Four sided polygons are called quadrilaterals. Sum of angles in a quadrilateral equals 360. Parallelogram is a quadrilateral where opposite sides are parallel.

More information

6-1. Angles of Polygons. Lesson 6-1. What You ll Learn. Active Vocabulary

6-1. Angles of Polygons. Lesson 6-1. What You ll Learn. Active Vocabulary 6-1 Angles of Polygons What You ll Learn Skim Lesson 6-1. Predict two things that you expect to learn based on the headings and figures in the lesson. 1. 2. Lesson 6-1 Active Vocabulary diagonal New Vocabulary

More information

CHARACTERISTICS AND CLASSIFICATION OF SHAPES and 1.3.2

CHARACTERISTICS AND CLASSIFICATION OF SHAPES and 1.3.2 CHARACTERISTICS AND CLASSIFICATION OF SHAPES 1.3.1 and 1.3.2 Geometric shapes occur in many places. After studying them using transformations, students start to see certain characteristics of different

More information

Downloaded from

Downloaded from 1 IX Mathematics Chapter 8: Quadrilaterals Chapter Notes Top Definitions 1. A quadrilateral is a closed figure obtained by joining four points (with no three points collinear) in an order. 2. A diagonal

More information

Downloaded from

Downloaded from Symmetry 1 1.A line segment is Symmetrical about its ---------- bisector (A) Perpendicular (B) Parallel (C) Line (D) Axis 2.How many lines of symmetry does a reactangle have? (A) Four (B) Three (C)

More information

Title: Quadrilaterals Aren t Just Squares

Title: Quadrilaterals Aren t Just Squares Title: Quadrilaterals ren t Just Squares Brief Overview: This is a collection of the first three lessons in a series of seven lessons studying characteristics of quadrilaterals, including trapezoids, parallelograms,

More information

Unit 6: Quadrilaterals

Unit 6: Quadrilaterals Name: Period: Unit 6: Quadrilaterals Geometry Honors Homework Section 6.1: Classifying Quadrilaterals State whether each statement is true or false. Justify your response. 1. All squares are rectangles.

More information

Regents Exam Questions G.G.69: Quadrilaterals in the Coordinate Plane 2

Regents Exam Questions G.G.69: Quadrilaterals in the Coordinate Plane 2 Regents Exam Questions G.G.69: Quadrilaterals in the Coordinate Plane 2 www.jmap.org Name: G.G.69: Quadrilaterals in the Coordinate Plane 2: Investigate the properties of quadrilaterals in the coordinate

More information

Page 3 of 26 Copyright 2014 by The McGraw-Hill Companies, Inc.

Page 3 of 26 Copyright 2014 by The McGraw-Hill Companies, Inc. 1. This picture shows the side of Allen's desk. What type of angle is made by the top of Allen's desk and one of the legs? A acute B obtuse C right D straight 2. Look at these two shapes on the grid. Draw

More information

Date: Period: Quadrilateral Word Problems: Review Sheet

Date: Period: Quadrilateral Word Problems: Review Sheet Name: Quadrilateral Word Problems: Review Sheet Date: Period: Geometry Honors Directions: Please answer the following on a separate sheet of paper. Completing this review sheet will help you to do well

More information

NCERT Solution Class 7 Mathematics Symmetry Chapter: 14. Copy the figures with punched holes and find the axes of symmetry for the following:

NCERT Solution Class 7 Mathematics Symmetry Chapter: 14. Copy the figures with punched holes and find the axes of symmetry for the following: Downloaded from Q.1) Exercise 14.1 NCERT Solution Class 7 Mathematics Symmetry Chapter: 14 Copy the figures with punched holes and find the axes of symmetry for the following: Sol.1) S.No. Punched holed

More information

Downloaded from

Downloaded from Symmetry 1.Can you draw a figure whose mirror image is identical to the figure itself? 2.Find out if the figure is symmetrical or not? 3.Count the number of lines of symmetry in the figure. 4.A line

More information

Geometry Tutor Worksheet 9 Quadrilaterals

Geometry Tutor Worksheet 9 Quadrilaterals Geometry Tutor Worksheet 9 Quadrilaterals 1 Geometry Tutor - Worksheet 9 - Quadrilaterals 1. Which name best describes quadrilateral DEFG? 2. Which name best describes quadrilateral ABCD? 3. Which name

More information

Secondary 2 Unit 7 Test Study Guide

Secondary 2 Unit 7 Test Study Guide Class: Date: Secondary 2 Unit 7 Test Study Guide 2014-2015 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which statement can you use to conclude that

More information

Geometer s Skethchpad 7th Grade Guide to Learning Geometry

Geometer s Skethchpad 7th Grade Guide to Learning Geometry Geometer s Skethchpad 7th Grade Guide to Learning Geometry This Guide Belongs to: Date: 2 -- Learning with Geometer s Sketchpad **a story can be added or one could choose to use the activities alone and

More information

Review Questions for Unit Exam 32 Geometry

Review Questions for Unit Exam 32 Geometry Review Questions for Unit Exam 32 Geometry 1.Intheaccompanyingdiagramof parallelogramabcd,diagonals AC and BD intersectate,ae&=3x& 4,andEC&=x&+12. Whatisthevalueofx? (1)8 (3)20 (2)16 (4)40 2.Intheaccompanyingdiagramof

More information

Grade 4 Math Unit 6: GEOMETRY. Standards Report. Student Name:

Grade 4 Math Unit 6: GEOMETRY. Standards Report. Student Name: Grade 4 Math Unit 6: GEOMETRY Standards Report Student Name: Standards MGSE4.G.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify

More information

Warm-Up Exercises. Find the value of x. 1. ANSWER 65 ANSWER 120

Warm-Up Exercises. Find the value of x. 1. ANSWER 65 ANSWER 120 Warm-Up Exercises Find the value of x. 1. 65 2. 120 Warm-Up Exercises Find the value of x. 3. 70 EXAMPLE Warm-Up 1Exercises Identify quadrilaterals Quadrilateral ABCD has at least one pair of opposite

More information

PENNSYLVANIA. List properties, classify, draw, and identify geometric figures in two dimensions.

PENNSYLVANIA. List properties, classify, draw, and identify geometric figures in two dimensions. Know: Understand: Do: CC.2.3.4.A.1 -- Draw lines and angles and identify these in two-dimensional figures. CC.2.3.4.A.2 -- Classify twodimensional figures by properties of their lines and angles. CC.2.3.4.A.3

More information

1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable

1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable Four sided polygon 1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable Foldable The fold crease 2. Now, divide the right hand section

More information

ISBN Copyright 2015 The Continental Press, Inc.

ISBN Copyright 2015 The Continental Press, Inc. Table of COntents Introduction 3 Format of Books 4 Suggestions for Use 7 Annotated Answer Key and Extension Activities 9 Reproducible Tool Set 175 ISBN 978-0-8454-8768-6 Copyright 2015 The Continental

More information

Geometry 1 FINAL REVIEW 2011

Geometry 1 FINAL REVIEW 2011 Geometry 1 FINL RVIW 2011 1) lways, Sometimes, or Never. If you answer sometimes, give an eample for when it is true and an eample for when it is not true. a) rhombus is a square. b) square is a parallelogram.

More information

Standard 4.G.1 4.G.2 5.G.3 5.G.4 4.MD.5

Standard 4.G.1 4.G.2 5.G.3 5.G.4 4.MD.5 Draw and identify lines and angles, as well as classify shapes by properties of their lines and angles (Standards 4.G.1 3). Standard 4.G.1 Draw points, lines, line segments, rays, angles (right, acute,

More information

Class VI Mathematics (Ex. 13.1) Questions

Class VI Mathematics (Ex. 13.1) Questions Class VI Mathematics (Ex. 13.1) Questions 1. List any four symmetrical from your home or school. 2. For the given figure, which one is the mirror line, l 1 or l 2? 3. Identify the shapes given below. Check

More information

Constructing Angle Bisectors and Parallel Lines

Constructing 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 information

GEO: Sem 1 Unit 1 Review of Geometry on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1)

GEO: Sem 1 Unit 1 Review of Geometry on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1) GEO: Sem 1 Unit 1 Review of Geometr on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1) NAME OJECTIVES: WARM UP Develop and appl the formula for midpoint. Use the Distance

More information

is formed where the diameters intersect? Label the center.

is formed where the diameters intersect? Label the center. E 26 Get Into Shape Hints or notes: A circle will be folded into a variety of geometric shapes. This activity provides the opportunity to assess the concepts, vocabulary and knowledge of relationships

More information

Honors Geometry Chapter 6 Supplement. Q (4x) (5x)

Honors Geometry Chapter 6 Supplement. Q (4x) (5x) Honors Geometry hapter 6 upplement Name: 1. Given: Q m Q = (4x) m Q = (5x) m Q = 40 m Q = 32 Find the value of x, m Q, m Q, m Q Q (4x) (5x) 40 32 2. Given: m = (8x + 20) m = (150 6x) m = (12x + 60) a)

More information

Geometry Unit 5 Practice Test

Geometry Unit 5 Practice Test Name: Class: Date: ID: X Geometry Unit 5 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the value of x in the rectangle? Hint: use

More information

Name Date Due Date. 1. Mark drew the following figures. Which figure has more than one line of symmetry? a. b. c. d.

Name Date Due Date. 1. Mark drew the following figures. Which figure has more than one line of symmetry? a. b. c. d. Name Date Due Date Go Math Chapter 10 Test Review Grade 4 1. Mark drew the following figures. Which figure has more than one line of symmetry? 2. Kate drew the following figures. Which figure has more

More information

Copying a Line Segment

Copying a Line Segment Copying a Line Segment Steps 1 4 below show you how to copy a line segment. Step 1 You are given line segment AB to copy. A B Step 2 Draw a line segment that is longer than line segment AB. Label one of

More information

Geometry Topic 4 Quadrilaterals and Coordinate Proof

Geometry Topic 4 Quadrilaterals and Coordinate Proof Geometry Topic 4 Quadrilaterals and Coordinate Proof MAFS.912.G-CO.3.11 In the diagram below, parallelogram has diagonals and that intersect at point. Which expression is NOT always true? A. B. C. D. C

More information

Lesson 3.1 Duplicating Segments and Angles

Lesson 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 information

11.2 Areas of Trapezoids,

11.2 Areas of Trapezoids, 11. Areas of Trapezoids, Rhombuses, and Kites Goal p Find areas of other types of quadrilaterals. Your Notes VOCABULARY Height of a trapezoid THEOREM 11.4: AREA OF A TRAPEZOID b 1 The area of a trapezoid

More information

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true? 0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB # AC. The measure of!b is 40. 1) a! b 2) a! c 3) b! c 4) d! e What is the measure of!a? 1) 40 2) 50 3) 70

More information

FINAL REVIEW. 1) Always, Sometimes, or Never. If you answer sometimes, give an example for when it is true and an example for when it is not true.

FINAL REVIEW. 1) Always, Sometimes, or Never. If you answer sometimes, give an example for when it is true and an example for when it is not true. FINL RVIW 1) lways, Sometimes, or Never. If you answer sometimes, give an eample for when it is true and an eample for when it is not true. a) rhombus is a square. b) square is a parallelogram. c) oth

More information

Unit 6 Quadrilaterals

Unit 6 Quadrilaterals Unit 6 Quadrilaterals ay lasswork ay Homework Monday Properties of a Parallelogram 1 HW 6.1 11/13 Tuesday 11/14 Proving a Parallelogram 2 HW 6.2 Wednesday 11/15 Thursday 11/16 Friday 11/17 Monday 11/20

More information

Trapezoids. are the bases. TP. / are the legs.

Trapezoids. are the bases. TP. / are the legs. 8 5 What You ll Learn You ll learn to identify and use the properties of trapezoids and isosceles trapezoids. rapezoids any state flags use geometric shapes in their designs. an you find a quadrilateral

More information

1. Use the following directions to draw a figure in the box to the right. a. Draw two points: and. b. Use a straightedge to draw.

1. Use the following directions to draw a figure in the box to the right. a. Draw two points: and. b. Use a straightedge to draw. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 1 Homework 4 Name Date 1. Use the following directions to draw a figure in the box to the right. a. Draw two points: and. b. Use a straightedge to draw. c.

More information

University of Houston High School Mathematics Contest Geometry Exam Spring 2016

University of Houston High School Mathematics Contest Geometry Exam Spring 2016 University of Houston High School Mathematics ontest Geometry Exam Spring 016 nswer the following. Note that diagrams may not be drawn to scale. 1. In the figure below, E, =, = 4 and E = 0. Find the length

More information

What You ll Learn. Why It s Important

What 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 information

1. Use the following directions to draw a figure in the box to the right. a. Draw two points: and. b. Use a straightedge to draw.

1. Use the following directions to draw a figure in the box to the right. a. Draw two points: and. b. Use a straightedge to draw. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 1 Problem Set 4 Name Date 1. Use the following directions to draw a figure in the box to the right. a. Draw two points: and. b. Use a straightedge to draw.

More information

Name. FORT SMITH SCHOOL DISTRICT Geometry / mod 3 review Math. Teacher Period. Use the figure below to answer question 1.

Name. FORT SMITH SCHOOL DISTRICT Geometry / mod 3 review Math. Teacher Period. Use the figure below to answer question 1. FORT SMITH SCHOOL DISTRICT Geometry / mod 3 review Math Use the figure below to answer question 1. Name Teacher Period 2. A television antenna is mounted on the peak of a roof. When standing 30 feet away

More information

Objective: Draw kites and squares to clarify their attributes, and define kites and squares based on those attributes.

Objective: 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 information

Geometric Constructions

Geometric 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 information

Fair Game Review. Chapter 7. Name Date

Fair Game Review. Chapter 7. Name Date Name Date Chapter 7 Fair Game Review Use a protractor to find the measure of the angle. Then classify the angle as acute, obtuse, right, or straight. 1. 2. 3. 4. 5. 6. 141 Name Date Chapter 7 Fair Game

More information

Save My Exams! The Home of Revision For more awesome GCSE and A level resources, visit us at Symmetry.

Save My Exams! The Home of Revision For more awesome GCSE and A level resources, visit us at   Symmetry. Symmetry Question Paper 1 Level IGCSE Subject Maths (0580) Exam Board Cambridge International Examinations (CIE) Paper Type Extended Topic Geometry Sub-Topic Symmetry (inc. Circles) Booklet Question Paper

More information

1. What term describes a transformation that does not change a figure s size or shape?

1. What term describes a transformation that does not change a figure s size or shape? 1. What term describes a transformation that does not change a figure s size or shape? () similarity () isometry () collinearity (D) symmetry For questions 2 4, use the diagram showing parallelogram D.

More information

3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm.

3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. 1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify

More information

STRAND H: Angle Geometry

STRAND 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 information

Length and area Block 1 Student Activity Sheet

Length and area Block 1 Student Activity Sheet Block 1 Student Activity Sheet 1. Write the area and perimeter formulas for each shape. 2. What does each of the variables in these formulas represent? 3. How is the area of a square related to the area

More information

Geometry - Chapter 6 Review

Geometry - Chapter 6 Review Class: Date: Geometry - Chapter 6 Review 1. Find the sum of the measures of the angles of the figure. 4. Find the value of x. The diagram is not to scale. A. 1260 B. 900 C. 540 D. 720 2. The sum of the

More information

9.5 Properties and Conditions for Kites and Trapezoids

9.5 Properties and Conditions for Kites and Trapezoids Name lass ate 9.5 Properties and onditions for Kites and Trapezoids ssential uestion: What are the properties of kites and trapezoids? Resource Locker xplore xploring Properties of Kites kite is a quadrilateral

More information

Extra Practice 1. Name Date. Lesson 8.1: Parallel Lines. 1. Which line segments are parallel? How do you know? a) b) c) d)

Extra Practice 1. Name Date. Lesson 8.1: Parallel Lines. 1. Which line segments are parallel? How do you know? a) b) c) d) Master 8.24 Extra Practice 1 Lesson 8.1: Parallel Lines 1. Which line segments are parallel? How do you know? a) b) c) d) 2. Look at the diagram below. Find as many pairs of parallel line segments as you

More information

Name. Ms. Nong. Due on: Per: Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0

Name. 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 information

Geometry 2001 part 1

Geometry 2001 part 1 Geometry 2001 part 1 1. Point is the center of a circle with a radius of 20 inches. square is drawn with two vertices on the circle and a side containing. What is the area of the square in square inches?

More information

Name Date # 1 Exit Tickets 5.5

Name Date # 1 Exit Tickets 5.5 Name Date # 1 1. What is the volume of the figures pictured below? 2. Draw a picture of a figure with a volume of 3 cubic units on the dot paper. Name Date # 2 1. If this net were to be folded into a box,

More information

Materials: Computer lab or set of calculators equipped with Cabri Geometry II and lab worksheet.

Materials: Computer lab or set of calculators equipped with Cabri Geometry II and lab worksheet. Constructing Perpendiculars Lesson Summary: Students will complete the basic compass and straight edge constructions commonly taught in first year high school Geometry. Key Words: perpendicular, compass,

More information

6.2 Slopes of Parallel and Perpendicular Lines

6.2 Slopes of Parallel and Perpendicular Lines . Slopes of Parallel and Perpendicular Lines FOCUS Use slope to find out if two lines are parallel or perpendicular. These two lines are parallel. Slope of line AB Slope of line CD These two lines have

More information

Worksheet 10 Memorandum: Construction of Geometric Figures. Grade 9 Mathematics

Worksheet 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 information

Parallels and Euclidean Geometry

Parallels and Euclidean Geometry Parallels and Euclidean Geometry Lines l and m which are coplanar but do not meet are said to be parallel; we denote this by writing l m. Likewise, segments or rays are parallel if they are subsets of

More information

Cross Sections of Three-Dimensional Figures

Cross Sections of Three-Dimensional Figures Domain 4 Lesson 22 Cross Sections of Three-Dimensional Figures Common Core Standard: 7.G.3 Getting the Idea A three-dimensional figure (also called a solid figure) has length, width, and height. It is

More information

Areas of Tropezoids, Rhombuses, and Kites

Areas of Tropezoids, Rhombuses, and Kites 102 Areas of Tropezoids, Rhombuses, and Kites MathemaHcs Florida Standards MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MP1. MP3, MP 4,MP6 Objective

More information

5.3. Area of Polygons and Circles Play Area. My Notes ACTIVITY

5.3. Area of Polygons and Circles Play Area. My Notes ACTIVITY Area of Polygons and Circles SUGGESTED LEARNING STRATEGIES: Think/Pair/Share ACTIVITY 5.3 Pictured below is an aerial view of a playground. An aerial view is the view from above something. Decide what

More information

16. DOK 1, I will succeed." In this conditional statement, the underlined portion is

16. 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 information

Name: Section: Tuesday January 17 th 10.6 (1 page) Wednesday January 18 th 10.7 (1 page) Thursday January 19 th Chapter 10 Study Guide (2 pages)

Name: Section: Tuesday January 17 th 10.6 (1 page) Wednesday January 18 th 10.7 (1 page) Thursday January 19 th Chapter 10 Study Guide (2 pages) Homework Hello Students and Parents. We will continue learning about Two-Dimensional Shapes. Students will identify and draw lines of symmetry in two-dimensional figures. Students will describe patterns

More information

GeoGebra. Before we begin. Dynamic Mathematics for Schools

GeoGebra. Before we begin. Dynamic Mathematics for Schools Before we begin Start your favorite internet browser If is not installed: Go to www.geogebra.org Click WebStart (third item down in the menu on the left) Click the WebStart button ( is installed automatically)

More information

1 st Subject: 2D Geometric Shape Construction and Division

1 st Subject: 2D Geometric Shape Construction and Division Joint Beginning and Intermediate Engineering Graphics 2 nd Week 1st Meeting Lecture Notes Instructor: Edward N. Locke Topic: Geometric Construction 1 st Subject: 2D Geometric Shape Construction and Division

More information

The Quadrilateral Detective

The Quadrilateral Detective The Quadrilateral Detective a Coordinate Geometry Activity An object might certainly LOOK like a square, but how much information do you really need before you can be absolutely sure that it IS a square?

More information

CTB/McGraw-Hill. Math Quarter 2: Week 5: Mixed Review Test ID:

CTB/McGraw-Hill. Math Quarter 2: Week 5: Mixed Review Test ID: Page 1 of 35 Developed and published by CTB/McGraw-Hill LLC, a subsidiary of The McGraw-Hill Companies, Inc., 20 Ryan Ranch Road, Monterey, California 93940-5703. All rights reserved. Only authorized customers

More information

LIST OF HANDS-ON ACTIVITIES IN MATHEMATICS FOR CLASSES III TO VIII. Mathematics Laboratory

LIST OF HANDS-ON ACTIVITIES IN MATHEMATICS FOR CLASSES III TO VIII. Mathematics Laboratory LIST OF HANDS-ON ACTIVITIES IN MATHEMATICS FOR CLASSES III TO VIII Mathematics Laboratory The concept of Mathematics Laboratory has been introduced by the Board in its affiliated schools with the objective

More information

0810ge. Geometry Regents Exam y # (x $ 3) 2 % 4 y # 2x $ 5 1) (0,%4) 2) (%4,0) 3) (%4,%3) and (0,5) 4) (%3,%4) and (5,0)

0810ge. Geometry Regents Exam y # (x $ 3) 2 % 4 y # 2x $ 5 1) (0,%4) 2) (%4,0) 3) (%4,%3) and (0,5) 4) (%3,%4) and (5,0) 0810ge 1 In the diagram below, ABC! XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements

More information

Geometry by Jurgensen, Brown and Jurgensen Postulates and Theorems from Chapter 1

Geometry 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 information

Geometer s Skethchpad 8th Grade Guide to Learning Geometry

Geometer 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 information

Homework Chapter 14. Areas. Exercise 1. TeeJay Publishers General Homework for Book 3G Ch 14 - Areas

Homework Chapter 14. Areas. Exercise 1. TeeJay Publishers General Homework for Book 3G Ch 14 - Areas Areas Homework Chapter 14 Exercise 1 1. Write down the areas (in cm 2 ) of each of the following shapes : = 1 cm 2 (e) 2. Find the shaded area in each of these :- 3. Write down the areas of these two shapes

More information

The area A of a trapezoid is one half the product of the height h and the sum of the lengths of its bases, b 1 and b 2.

The area A of a trapezoid is one half the product of the height h and the sum of the lengths of its bases, b 1 and b 2. ALGEBRA Find each missing length. 21. A trapezoid has a height of 8 meters, a base length of 12 meters, and an area of 64 square meters. What is the length of the other base? The area A of a trapezoid

More information

(A) Circle (B) Polygon (C) Line segment (D) None of them (A) (B) (C) (D) (A) Understanding Quadrilaterals <1M>

(A) Circle (B) Polygon (C) Line segment (D) None of them (A) (B) (C) (D) (A) Understanding Quadrilaterals <1M> Understanding Quadrilaterals 1.A simple closed curve made up of only line segments is called a (A) Circle (B) Polygon (C) Line segment (D) None of them 2.In the following figure, which of the polygon

More information

The Texas Education Agency and the Texas Higher Education Coordinating Board Geometry Module Pre-/Post-Test. U x T'

The Texas Education Agency and the Texas Higher Education Coordinating Board Geometry Module Pre-/Post-Test. U x T' Pre-/Post-Test The Texas Education Agency and the Texas Higher Education Coordinating Board Geometry Module Pre-/Post-Test 1. Triangle STU is rotated 180 clockwise to form image STU ' ' '. Determine the

More information

Kenmore-Town of Tonawanda UFSD. We educate, prepare, and inspire all students to achieve their highest potential

Kenmore-Town of Tonawanda UFSD. We educate, prepare, and inspire all students to achieve their highest potential Kenmore-Town of Tonawanda UFSD We educate, prepare, and inspire all students to achieve their highest potential Grade 2 Module 8 Parent Handbook The materials contained within this packet have been taken

More information

(A) Circle (B) Polygon (C) Line segment (D) None of them

(A) Circle (B) Polygon (C) Line segment (D) None of them Understanding Quadrilaterals 1.The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60 degree. Find the angles of the parallelogram.

More information

Class : VI - Mathematics

Class : VI - Mathematics O. P. JINDAL SCHOOL, RAIGARH (CG) 496 001 Phone : 07762-227042, 227293, (Extn. 227001-49801, 02, 04, 06); Fax : 07762-262613; e-mail: opjsraigarh@jspl.com; website : www.opjsrgh.in Class : VI - Mathematics

More information

(Length and Area Ratio s)

(Length and Area Ratio s) (Length and Area Ratio s) Standard Televisions are measured by the length of the diagonal. Most manufactures included the TV frame as part of the measurement (when measuring CRT (cathode ray tube) screens).

More information

CATHY HUMPHREYS: Ah, opposite sides are not parallel. So there we go. What do we know from that?

CATHY HUMPHREYS: Ah, opposite sides are not parallel. So there we go. What do we know from that? Tuesday Group Work Part E: STUDENT: We have two pairs of congruent sides. CATHY HUMPHREYS: So how do you know that a rhombus cannot be a kite? And I want you to refer to the definitions because that is

More information

Geometer s Sketchpad Version 4

Geometer s Sketchpad Version 4 Geometer s Sketchpad Version 4 For PC Name: Date: INVESTIGATION: The Pythagorean Theorem Directions: Use the steps below to lead you through the investigation. After each step, be sure to click in the

More information

June 2016 Regents GEOMETRY COMMON CORE

June 2016 Regents GEOMETRY COMMON CORE 1 A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object below is generated by this rotation? 4) 2

More information

Objective: Draw trapezoids to clarify their attributes, and define trapezoids based on those attributes.

Objective: Draw trapezoids to clarify their attributes, and define trapezoids based on those attributes. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 16 5 5 Lesson 16 Objective: Draw trapezoids to clarify their attributes, and define trapezoids based Suggested Lesson Structure Fluency Practice Application

More information

Find and Draw Lines. How do you find lines of symmetry? STEP 2

Find and Draw Lines. How do you find lines of symmetry? STEP 2 ? Name 13.6 Essential Question Find and raw Lines of Symmetry How do you find lines of symmetry? Geometry and Measurement 4.6. MTHEMTIL PROESSES 4.1., 4.1.F, 4.1.G Unlock the Problem How many lines of

More information

Exploring Special Lines (Pappus, Desargues, Pascal s Mystic Hexagram)

Exploring Special Lines (Pappus, Desargues, Pascal s Mystic Hexagram) Exploring Special Lines (Pappus, Desargues, Pascal s Mystic Hexagram) Introduction These three lab activities focus on some of the discoveries made by famous mathematicians by investigating lines. The

More information

SOLUTION: The trapezoid ABCD is an isosceles trapezoid. So, each pair of base angles is congruent. Therefore,

SOLUTION: The trapezoid ABCD is an isosceles trapezoid. So, each pair of base angles is congruent. Therefore, Find each measure. 1. The trapezoid ABCD is an isosceles trapezoid. So, each pair of base angles is congruent. Therefore, 2. WT, if ZX = 20 and TY = 15 The trapezoid WXYZ is an isosceles trapezoid. So,

More information

3. Given the similarity transformation shown below; identify the composition:

3. 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 information

Geometry Mrs. Crocker Spring 2014 Final Exam Review

Geometry Mrs. Crocker Spring 2014 Final Exam Review Name: Mod: Geometry Mrs. Crocker Spring 2014 Final Exam Review Use this exam review to complete your flip book and to study for your upcoming exam. You must bring with you to the exam: 1. Pencil, eraser,

More information

Please plan carefully. Papers are due at the start of class on the due date. Late papers will not be accepted.

Please plan carefully. Papers are due at the start of class on the due date. Late papers will not be accepted. Please plan carefully. Papers are due at the start of class on the due date. Late papers will not be accepted. Name: Geometry CC Regents Review #11 Part I: Answer all questions in this part. Each correct

More information

Name Date. Chapter 15 Final Review

Name Date. Chapter 15 Final Review Name Date Chapter 15 Final Review Tell whether the events are independent or dependent. Explain. 9) You spin a spinner twice. First Spin: You spin a 2. Second Spin: You spin an odd number. 10) Your committee

More information

Objective: Draw rectangles and rhombuses to clarify their attributes, and define rectangles and rhombuses based on those attributes.

Objective: 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 information

Trapezoids and Kites. isosceles trapezoid. You are asked to prove the following theorems in the exercises.

Trapezoids and Kites. isosceles trapezoid. You are asked to prove the following theorems in the exercises. Page 1 of 8 6.5 Trapezoids and ites What you should learn O 1 Use properties of trapezoids. O 2 Use properties of kites. Why you should learn it To solve real-life problems, such as planning the layers

More information

Measuring and Drawing Angles and Triangles

Measuring 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 information

Mathematics 43601F. Geometry. In the style of General Certificate of Secondary Education Foundation Tier. Past Paper Questions by Topic TOTAL

Mathematics 43601F. Geometry. In the style of General Certificate of Secondary Education Foundation Tier. Past Paper Questions by Topic TOTAL Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials In the style of General Certificate of Secondary Education Foundation Tier Pages 2 3 4 5 Mark

More information