Foundations of Math II Unit 3: Similarity and Congruence
|
|
- Maud Bryan
- 5 years ago
- Views:
Transcription
1 Foundations of Math II Unit 3: Similarity and Congruence Academics High School Mathematics
2 3.1 Warm Up 1. Jill and Bill are doing some exercises. Jayne Funda, their instructor, gently implores Touch your nose to your knees, maggots! Their attempts to please Ms. Funda are shown below. Bills says, I m doing better than you, Jill. My nose is much closer to my knees! Jill replies, That isn t a fair comparison, Bill. With whom do you agree? Who is doing a better job? Explain your answer. Jill Bill 2. The perimeter of ΔCOW is 12 units. a) Find possible lengths for CO, OW, and CW. b) Find four more sets of possible lengths. c) How many answers are possible? Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii 1
3 2
4 3
5 4
6 5
7 3.2 Warm Up 1. Which of the figures below could be the image of figure a when dilated? Explain why or why not for each figure. p g a c e r f s 2) a) Draw a line that passes through the origin of a coordinate plane and forms a 45 angle with the x-axis. b) Find the coordinates of at least three points on the line. c) Write an equation for the line. What do you notice? Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii 6
8 3.2 Practice with Dilations on the Coordinate Plane Graph three points that lie in three different quadrants and connect them to form a triangle. Label the vertices of the triangle as TRI. Record the coordinates of the triangle in the table below. Then find and apply the algebraic rules for each of the scale factors listed below. Graph and label each image. Scale Factor Algebraic Rule (x, y) (x, y) (x, y) T (, ) T (, ) T (, ) T (, ) R (, ) R (, ) R (, ) R (, ) I (, ) I (, ) I (, ) I (, ) What would each scale factor be if written as a percent? 7
9 Explain why or why not for each pair. 8
10 Find the scale factor. The pre-image is indicated by an arrow. 9
11 3.3 Warm Up 1. Draw each of the following dilations of quadrilateral BRIA: a. 150% scale factor using center X. b.!! scale factor using center Y. c. 1.5 scale factor using center I. d. What do you notice? A B X Y I R Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii 10
12 11
13 12
14 13
15 14
16 15
17 16
18 17
19 3.4 Warm Up 1. ΔRAP is an image of ΔCON using a dilation. Find point Z, the center of dilation, and also the scale factor. C O A R N P Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii 18
20 3.4 Investigation: Geometric Mean 1. Use your protractor to find the measure of the following angles. m ABC = m BCD = m CAB = m BDC = m ADC = m BCD= m DCA= What type of segment is CD called in ABC? What kind of triangles are ΔABC, ΔADC, and ΔBDC? 1. Trace ABC with a ruler on patty paper and carefully cut out ADC and BDC. You will need to place the letter of each vertex in the interior of each triangle on the patty paper so that you can still tell what you are working with after you cut it out (see below). 2. Next trace and cut out ABC. Be sure to label each vertex in the interior of the triangle. 3. Stack the cut out triangles so that that corresponding sides match up. Note that the three right triangles are similar to each other. Write a similarity statement for the three triangles. ΔABC 19
21 We know that the ratios of corresponding sides of similar triangles are proportional,!" 4. Using BDC and ΔCDA fill in the proportion: =!" So DC must be the geometric mean of and. 5. Using BDC and ABC fill in the proportion:!"!" = So BC must be the geometric mean of and. 6. Using ADC and ABC, fill in the proportion:!"!" = So AC must be the geometric mean of and. a h b m n c 7. Write three proportions for the picture above using what you learned from this activity. 20
22 Geometric Mean: Example Problems
23 3.4 Geometric Mean Practice 22
24 23
25 3.5 Warm Up 1) a) If a line has a slope greater than 1, what angle might it make with the x-axis? b) If a line has a slope less than 1, what angle might it make with the x-axis? c) If a line has a slope equal to 1, what angle might it make with the x-axis? Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii 24
26 3.5 Midsegment Example Problems Example 1 Find x. Example 2 DE is the midsegment of ΔABC. Find x, AC, and ED. 7x 28 Example 3 MN is the midsegment of ΔJKL. MN = 2x + 1 KJ = 5x 8 Find x, MN, and KJ. Example 4 25
27 3.5 Midsegments Show What You Know! 1) XY is the midsegment of ΔRST. Find each requested measure based on the given information. a) XY = 16, RS =? b) RS = 22, XY =? c) XY = 5x, RS = 15, x =? d) m R = 23, m TXY =? e) m XYS = 137, m YSR 2) Find x and y. 3) Find MS, PT, and ST. 3y 18 4) a) b) c) 26
28 3.6 Warm Up 1) a) A line forms an angle measuring less than 45 with the x-axis. What might its slope be? b) A line forms an angle measuring more than 45, but less than 90, with the x-axis. What might its slope be? c) What might the slope be if the line forms an obtuse angle with the x-axis? Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii 27
29 28
30 29
31 3.7 Warm Up 1) A line passes through the origin and the point A(7, 3). Without graphing the line, what can you conclude about the angle it will form with the x-axis? Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii 30
32 31
33 32
34 33
35 34
36 35
37 36
38 37
39 38
40 3.9 Flow Proof Examples 1) C is the midpoint of AD A D 1 2 AC DC ΔABC 2) MN PT 3 4 NO TO 1 2 ΔMNO 3) BD bisects ABC BD BD ABD CBD AB CB ΔABD 39
41 4) E is the midpoint of AD A D B C AE DE ΔABE 5) AS bisects MP Reflexive Property of Congruence Given ΔMAS 6) Given Definition of Angle Bisector ΔABD 40
42 3.10 Warm- up 1. Erica builds a ramp that makes a 45 with the ground. Her support board is 10 feet from the beginning of the ramp. a. How high is her support board? b. How long is her ramp? 2. Line m forms a 40 angle with the x- axis. Find the slope of line m. Explain your answer? Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii 41
43 3.10 Practice 1) C is the midpoint of BE C is the midpoint of AD ΔABC ΔDEC 2) 1 and 2 are right angles AD CB 3) All right angles are congruent ΔABD ΔCDB AB A S S Converse of the Isosceles Triangle Theorem ΔABD ΔCBD 42
44 3.11 Warm Up 1) Bill builds a ramp at a 56 angle with the ground. He uses a 12-foot support board and finds that the support board must be 8 feet from the beginning of the ramp in order to make the 56 angle. Jill also builds a ramp at a 56 angle with the ground. She uses a 9-foot support board. How far should her board be from the beginning of her ramp? Illustrate and explain your answer. Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii 43
45 Vocabulary Word Definition Characteristics Picture and/or Symbol Real Life Examples AAS ASA congruent dilation 44
46 Vocabulary Word Definition Characteristics Picture and/or Symbol Real Life Examples extremes flow proof geometric mean means 45
47 Vocabulary Word Definition Characteristics Picture and/or Symbol Real Life Examples midsegment Midsegment Theorem proof proportion 46
48 Vocabulary Word Definition Characteristics Picture and/or Symbol Real Life Examples SAS scale factor side similar 47
49 Vocabulary Word Definition Characteristics Picture and/or Symbol Real Life Examples SSS triangle Triangle Angle Sum Theorem vertex 48
50 Vocabulary Word Definition Characteristics Picture and/or Symbol Real Life Examples 49
51 50
Foundations of Math II Unit 3: Similarity and Congruence
Foundations of Math II Unit 3: Similarity and Congruence Academics High School Mathematics 3.1 Warm Up 1. Jill and Bill are doing some exercises. Jayne Funda, their instructor, gently implores Touch your
More information6-1. 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 informationGeometry - 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 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 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 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 informationGeometry 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 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 informationAnalytic Geometry EOC Study Booklet Geometry Domain Units 1-3 & 6
DOE Assessment Guide Questions (2015) Analytic Geometry EOC Study Booklet Geometry Domain Units 1-3 & 6 Question Example Item #1 Which transformation of ΔMNO results in a congruent triangle? Answer Example
More information3 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 informationEXT#2 ws Vertex Form of a Quadratic is Due TODAY HW#13 p222 / 1-14, 20 is due Tuesday Oct 21
Monday Oct 20, 2014 Take out your notebook for today's warm - up! EXT#2 ws Vertex Form of a Quadratic is Due TODAY HW#13 p222 / 1-14, 20 is due Tuesday Oct 21 Did you miss the QUIZ on Angles in a Triangle
More information6-6 Trapezoids and Kites. CCSS SENSE-MAKING If WXYZ is a kite, find each measure. 25. WP
CCSS SENSE-MAKING If WXYZ is a kite, find each measure. 25. WP By the Pythagorean Theorem, WP 2 = WX 2 XP 2 = 6 2 4 2 = 20 27. A kite can only have one pair of opposite congruent angles and Let m X = m
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 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 informationb. Draw a line and a circle that intersect at exactly one point. When this happens, the line is called a tangent.
6-1. Circles can be folded to create many different shapes. Today, you will work with a circle and use properties of other shapes to develop a three-dimensional shape. Be sure to have reasons for each
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 informationB. Examples: 1. At NVHS, there are 104 teachers and 2204 students. What is the approximate teacher to student ratio?
Name Date Period Notes Formal Geometry Chapter 7 Similar Polygons 7.1 Ratios and Proportions A. Definitions: 1. Ratio: 2. Proportion: 3. Cross Products Property: 4. Equivalent Proportions: B. Examples:
More informationGeometry Midterm Review Spring 2011 Name Date Period. 2. Name three points that are collinear Name a pair of opposite rays. 3.
Name Date Period Unit 1 1. Give two other names for AB. 1. 2. Name three points that are collinear. 2. 3. Name a pair of opposite rays. 3. 4. Give another name for CD. 4. Point J is between H and K on
More information0810ge. 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 informationUNDERSTAND SIMILARITY IN TERMS OF SIMILARITY TRANSFORMATIONS
UNDERSTAND SIMILARITY IN TERMS OF SIMILARITY TRANSFORMATIONS KEY IDEAS 1. A dilation is a transformation that makes a figure larger or smaller than the original figure based on a ratio given by a scale
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 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 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 information0809ge. 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 informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, :15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationHANDS-ON TRANSFORMATIONS: DILATIONS AND SIMILARITY (Poll Code 44273)
HANDS-ON TRANSFORMATIONS: DILATIONS AND SIMILARITY (Poll Code 44273) Presented by Shelley Kriegler President, Center for Mathematics and Teaching shelley@mathandteaching.org Fall 2014 8.F.1 8.G.3 8.G.4
More informationHANDS-ON TRANSFORMATIONS: RIGID MOTIONS AND CONGRUENCE (Poll Code 39934)
HANDS-ON TRANSFORMATIONS: RIGID MOTIONS AND CONGRUENCE (Poll Code 39934) Presented by Shelley Kriegler President, Center for Mathematics and Teaching shelley@mathandteaching.org Fall 2014 8.F.1 8.G.1a
More informationWhat s a Widget? EXAMPLE A L E S S O N 1.3
Page 1 of 7 L E S S O N 1.3 What s a Widget? Good definitions are very important in geometry. In this lesson you will write your own geometry definitions. Which creatures in the last group are Widgets?
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 informationGeometry Chapter 8 8-5: USE PROPERTIES OF TRAPEZOIDS AND KITES
Geometry Chapter 8 8-5: USE PROPERTIES OF TRAPEZOIDS AND KITES Use Properties of Trapezoids and Kites Objective: Students will be able to identify and use properties to solve trapezoids and kites. Agenda
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 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 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 informationDownloaded 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 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 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 informationBig Ideas Math: A Common Core Curriculum Geometry 2015 Correlated to Common Core State Standards for High School Geometry
Common Core State s for High School Geometry Conceptual Category: Geometry Domain: The Number System G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment,
More informationExtra 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 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 informationName Date Class Period. 5.2 Exploring Properties of Perpendicular Bisectors
Name Date Class Period Activity B 5.2 Exploring Properties of Perpendicular Bisectors MATERIALS QUESTION EXPLORE 1 geometry drawing software If a point is on the perpendicular bisector of a segment, is
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 informationUnit 7 Scale Drawings and Dilations
Unit 7 Scale Drawings and Dilations Day Classwork Day Homework Friday 12/1 Unit 6 Test Monday 12/4 Tuesday 12/5 Properties of Scale Drawings Scale Drawings Using Constructions Dilations and Scale Drawings
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 informationGeometry Semester 2 Final Review
Class: Date: Geometry Semester 2 Final Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Each unit on the map represents 5 miles. What
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 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 informationGEOMETRY. Workbook Common Core Standards Edition. Published by TOPICAL REVIEW BOOK COMPANY. P. O. Box 328 Onsted, MI
Workbook Common Core Standards Edition Published by TOPICAL REVIEW BOOK COMPANY P. O. Box 328 Onsted, MI 49265-0328 www.topicalrbc.com EXAM PAGE Reference Sheet...i January 2017...1 June 2017...11 August
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 informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 17, :30 to 3:30 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 17, 2017 12:30 to 3:30 p.m., only Student Name: School Name: The possession or use of any communications
More information6.1 Ratios, Proportions, and the Geometric Mean
6.1 Ratios, Proportions, and the Geometric Mean VOCABULARY Ratio of a to b Proportion Means and Extremes Geometric Mean EX1: Simplify Ratios Simplify the ratio. (See Table of Measures, p. 921) a. 76 cm:
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 informationGeometry Chapter 5 study guide
Geometry Chapter 5 study guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A right triangle is placed in a convenient position in the first quadrant
More informationHands-On Explorations of Plane Transformations
Hands-On Explorations of Plane Transformations James King University of Washington Department of Mathematics king@uw.edu http://www.math.washington.edu/~king The Plan In this session, we will explore exploring.
More informationTERRA Environmental Research Institute
TERRA Environmental Research Institute MATHEMATICS FCAT PRACTICE STRAND 3 Geometry and Spatial Sense Angle Relationships Lines and Transversals Plane Figures The Pythagorean Theorem The Coordinate Plane
More information2. Here are some triangles. (a) Write down the letter of the triangle that is. right-angled, ... (ii) isosceles. ... (2)
Topic 8 Shapes 2. Here are some triangles. A B C D F E G (a) Write down the letter of the triangle that is (i) right-angled,... (ii) isosceles.... (2) Two of the triangles are congruent. (b) Write down
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION Large-Type Edition GEOMETRY Friday, August 17, 2018 12:30 to 3:30 p.m., only Student Name: School Name: The possession or use of
More informationStandards of Learning Guided Practice Suggestions. For use with the Mathematics Tools Practice in TestNav TM 8
Standards of Learning Guided Practice Suggestions For use with the Mathematics Tools Practice in TestNav TM 8 Table of Contents Change Log... 2 Introduction to TestNav TM 8: MC/TEI Document... 3 Guided
More informationGeometry 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 informationSpecial Right Triangles and Right Triangle Trigonometry
Special Right Triangles and Right Triangle Trigonometry Reporting Category Topic Triangles Investigating special right triangles and right triangle trigonometry Primary SOL G.8 The student will solve real-world
More information, N NO FE. 7. Write a conjecture about two triangles with congruent angles.
Part 1: Is AAA a Similarity Shortcut? In this activity you will explore the following question: If three angles of one triangle are congruent to three corresponding angles of another triangle, are the
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 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 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 information5.3 Angle Bisectors in Triangles
5.3 Angle Bisectors in Triangles Learning Objectives Apply the Angle Bisector Theorem and its converse. Understand concurrency for angle bisectors. Review Queue 1. Construct the angle bisector of an 80
More informationMATHEMATICS: PAPER II
NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 2017 MATHEMATICS: PAPER II EXAMINATION NUMBER Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of
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 informationGeometry Final Exam Review 2012 #
1 PART 1: Multiple Choice (40 x 2 points = 80%). PART 2: Open Ended (2 x 10 = 20%) 1) Find the volume and surface area of the following rectangular prisms 2) Find the surface area of the following cylinders.
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 informationUsing inductive reasoning and conjectures Student Activity Sheet 2; use with Exploring The language of geometry
1. REINFORCE Find a geometric representation for the following sequence of numbers. 3, 4, 5, 6, 7, 2. What are the three undefined terms in geometry? 3. Write a description of a point. How are points labeled?
More informationFSA Geometry EOC Getting ready for. Circles, Geometric Measurement, and Geometric Properties with Equations.
Getting ready for. FSA Geometry EOC Circles, Geometric Measurement, and Geometric Properties with Equations 2014-2015 Teacher Packet Shared by Miami-Dade Schools Shared by Miami-Dade Schools MAFS.912.G-C.1.1
More informationGEOMETRY (Common Core)
GEOMETRY (COMMON CORE) Network 603 PRACTICE REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Practice Exam Student Name: School Name: The possession or use of any communications device is strictly
More informationAGS Math Algebra 2 Correlated to Kentucky Academic Expectations for Mathematics Grades 6 High School
AGS Math Algebra 2 Correlated to Kentucky Academic Expectations for Mathematics Grades 6 High School Copyright 2008 Pearson Education, Inc. or its affiliate(s). All rights reserved AGS Math Algebra 2 Grade
More informationLesson 3A. Opening Exercise. Identify which dilation figures were created using r = 1, using r > 1, and using 0 < r < 1.
: Properties of Dilations and Equations of lines Opening Exercise Identify which dilation figures were created using r = 1, using r > 1, and using 0 < r < 1. : Properties of Dilations and Equations of
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 informationWarm-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 information8.2 Slippery Slopes. A Solidify Understanding Task
7 8.2 Slippery Slopes A Solidify Understanding Task CC BY https://flic.kr/p/kfus4x While working on Is It Right? in the previous module you looked at several examples that lead to the conclusion that the
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 informationPage 1 of 1-7 Equations Teks Focus TEKS (2)(B) Derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity
More informationSimilar Figures 2.5. ACTIVITY: Reducing Photographs. How can you use proportions to help make decisions in art, design, and magazine layouts?
.5 Similar Figures How can you use proportions to help make decisions in art, design, and magazine layouts? In a computer art program, when you click and drag on a side of a photograph, you distort it.
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 informationDo Now: Do Now Slip. Do Now. Lesson 20. Drawing Conclusions. Quiz Tomorrow, Study Blue Sheet. Module 1 Lesson 20 Extra Practice.
Lesson 20 Drawing Conclusions HW Quiz Tomorrow, Study Blue Sheet Do Now: Do Now Slip Oct 20 1:03 PM Do Now 1. CB is parallel to DE 2.
More informationTitle: 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 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 informationKCATM Geometry
Name School KCATM Geometry 9 10 2013 1) Find the minimum perimeter of a rectangle whose area is 169 square meters. a) 42 meters b) 13 meters c) 26 meters d) 52 meters 2) Find the coordinates of the midpoint
More informationGEOMETRY CHAPTER 8 TEST
GEOMETRY CHAPTER 8 TEST NAME BLOCK DATE I,, hereby affirm that I neither gave nor received any help on this test. Furthermore, I used no sources of information to answer questions other than those explicitly
More informationOne of the classes that I have taught over the past few years is a technology course for
Trigonometric Functions through Right Triangle Similarities Todd O. Moyer, Towson University Abstract: This article presents an introduction to the trigonometric functions tangent, cosecant, secant, and
More information9.5 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 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 informationPolygon Unit Test Review
Name Hour Polygon Unit Test Review Directions: You must show all work for all problems below. For the problems where you have a quadrilateral and use their properties, justify the set up, and provide the
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 informationGEOMETRY (Common Core)
GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Wednesday, August 17, 2016 8:30 to 11:30 a.m., only Student Name: School Name: The
More informationPRE-JUNIOR CERTIFICATE EXAMINATION, 2010 MATHEMATICS HIGHER LEVEL. PAPER 2 (300 marks) TIME : 2½ HOURS
J.20 PRE-JUNIOR CERTIFICATE EXAMINATION, 2010 MATHEMATICS HIGHER LEVEL PAPER 2 (300 marks) TIME : 2½ HOURS Attempt ALL questions. Each question carries 50 marks. Graph paper may be obtained from the superintendent.
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 informationAreas 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 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 information6. Which angles in the diagram are congruent to 1? Choose all that apply. 2. m YKZ
PRYZ is a rhombus. If RK = 5, RY = 13 and m YRZ = 67, find each measure. Quadrilateral GHJK is a rectangle and m 1 = 37. 1. KY 6. Which angles in the diagram are congruent to 1? Choose all that apply.
More information1 Version 2.0. Related Below-Grade and Above-Grade Standards for Purposes of Planning for Vertical Scaling:
Claim 1: Concepts and Procedures Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Content Domain: Geometry Target E [a]: Draw, construct,
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 information6-5 P R OV I N G R H O M B U S E S, R E C TA N G L E S, A N D S Q UA R E S
6-5 P R OV I N G R H O M B U S E S, R E C TA N G L E S, A N D S Q UA R E S Workbook page 261, number 13 Given: ABCD is a rectangle Prove: EDC ECD A D E B C Statements Reasons 1) ABCD is a rectangle 1)
More information