Five-Minute Check (over Lesson 4 3) CCSS Then/Now New Vocabulary Postulate 4.1: Side-Side-Side (SSS) Congruence Example 1: Use SSS to Prove Triangles

Size: px
Start display at page:

Download "Five-Minute Check (over Lesson 4 3) CCSS Then/Now New Vocabulary Postulate 4.1: Side-Side-Side (SSS) Congruence Example 1: Use SSS to Prove Triangles"

Transcription

1

2 Five-Minute Check (over Lesson 4 3) CCSS Then/Now New Vocabulary Postulate 4.1: Side-Side-Side (SSS) Congruence Example 1: Use SSS to Prove Triangles Congruent Example 2: Standard Test Example: SSS on the Coordinate Plane Postulate 4.2: Side-Angle-Side (SAS) Congruence Example 3: Real-World Example: Use SAS to Prove Triangles are Congruent Example 4: Use SAS or SSS in Proofs

3 Over Lesson 4 3 Write a congruence statement for the triangles. A. ΔLMN ΔRTS B. ΔLMN ΔSTR C. ΔLMN ΔRST D. ΔLMN ΔTRS

4 Over Lesson 4 3 Write a congruence statement for the triangles. A. ΔLMN ΔRTS B. ΔLMN ΔSTR C. ΔLMN ΔRST D. ΔLMN ΔTRS

5 Over Lesson 4 3 Name the corresponding congruent angles for the congruent triangles. A. L R, N T, M S B. L R, M S, N T C. L T, M R, N S D. L R, N S, M T

6 Over Lesson 4 3 Name the corresponding congruent angles for the congruent triangles. A. L R, N T, M S B. L R, M S, N T C. L T, M R, N S D. L R, N S, M T

7 Over Lesson 4 3 Name the corresponding congruent sides for the congruent triangles. A. LM RT, LN RS, NM ST B. LM RT, LN LR, LM LS C. LM ST, LN RT, NM RS D. LM LN, RT RS, MN ST

8 Over Lesson 4 3 Name the corresponding congruent sides for the congruent triangles. A. LM RT, LN RS, NM ST B. LM RT, LN LR, LM LS C. LM ST, LN RT, NM RS D. LM LN, RT RS, MN ST

9 Over Lesson 4 3 Refer to the figure. Find x. A. 1 B. 2 C. 3 D. 4

10 Over Lesson 4 3 Refer to the figure. Find x. A. 1 B. 2 C. 3 D. 4

11 Over Lesson 4 3 Refer to the figure. Find m A. A. 30 B. 39 C. 59 D. 63

12 Over Lesson 4 3 Refer to the figure. Find m A. A. 30 B. 39 C. 59 D. 63

13 Over Lesson 4 3 Given that ΔABC ΔDEF, which of the following statements is true? A. A E B. C D C. AB DE D. BC FD

14 Over Lesson 4 3 Given that ΔABC ΔDEF, which of the following statements is true? A. A E B. C D C. AB DE D. BC FD

15 Content Standards G.CO.10 Prove theorems about triangles. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 1 Make sense of problems and persevere in solving them.

16 You proved triangles congruent using the definition of congruence. Use the SSS Postulate to test for triangle congruence. Use the SAS Postulate to test for triangle congruence.

17 included angle

18

19 Write a flow proof. Use SSS to Prove Triangles Congruent Given: Prove: QU AD, QD AU ΔQUD ΔADU

20 Answer: Use SSS to Prove Triangles Congruent

21 Answer: Flow Proof: Use SSS to Prove Triangles Congruent

22 Which information is missing from the flowproof? Given: AC AB D is the midpoint of BC. Prove: ΔADC ΔADB A. AC AC B. AB AB C. AD AD D. CB BC

23 Which information is missing from the flowproof? Given: AC AB D is the midpoint of BC. Prove: ΔADC ΔADB A. AC AC B. AB AB C. AD AD D. CB BC

24 SSS on the Coordinate Plane EXTENDED RESPONSE Triangle DVW has vertices D( 5, 1), V( 1, 2), and W( 7, 4). Triangle LPM has vertices L(1, 5), P(2, 1), and M(4, 7). a. Graph both triangles on the same coordinate plane. b. Use your graph to make a conjecture as to whether the triangles are congruent. Explain your reasoning. c. Write a logical argument that uses coordinate geometry to support the conjecture you made in part b.

25 Read the Test Item You are asked to do three things in this problem. In part a, you are to graph ΔDVW and ΔLPM on the same coordinate plane. In part b, you should make a conjecture that ΔDVW ΔLPM or ΔDVW / ΔLPM based on your graph. Finally, in part c, you are asked to prove your conjecture. Solve the Test Item a. SSS on the Coordinate Plane

26 SSS on the Coordinate Plane b. From the graph, it appears that the triangles have the same shapes, so we conjecture that they are congruent. c. Use the Distance Formula to show all corresponding sides have the same measure.

27 SSS on the Coordinate Plane

28 Answer: SSS on the Coordinate Plane

29 SSS on the Coordinate Plane Answer: WD = ML, DV = LP, and VW = PM. By definition of congruent segments, all corresponding segments are congruent. Therefore, ΔDVW ΔLPM by SSS.

30 Determine whether ΔABC ΔDEF for A( 5, 5), B(0, 3), C( 4, 1), D(6, 3), E(1, 1), and F(5, 1). A. yes B. no C. cannot be determined

31 Determine whether ΔABC ΔDEF for A( 5, 5), B(0, 3), C( 4, 1), D(6, 3), E(1, 1), and F(5, 1). A. yes B. no C. cannot be determined

32

33 Use SAS to Prove Triangles are Congruent ENTOMOLOGY The wings of one type of moth form two triangles. Write a two-column proof to prove that ΔFEG ΔHIG if EI FH, and G is the midpoint of both EI and FH.

34 Use SAS to Prove Triangles are Congruent Given: EI FH; G is the midpoint of both EI and FH. Prove: ΔFEG ΔHIG Proof: Statements 1. EI FH; G is the midpoint of EI; G is the midpoint of FH. Reasons 1. Given FGE HGI 4. ΔFEG ΔHIG 2. Midpoint Theorem 3. Vertical Angles Theorem 4. SAS

35 The two-column proof is shown to prove that ΔABG ΔCGB if ABG CGB and AB CG. Choose the best reason to fill in the blank. Proof: Statements Reasons 1. Given 2.? Property 3. ΔABG ΔCGB 3. SSS A. Reflexive B. Symmetric C. Transitive D. Substitution

36 The two-column proof is shown to prove that ΔABG ΔCGB if ABG CGB and AB CG. Choose the best reason to fill in the blank. Proof: Statements Reasons 1. Given 2.? Property 3. ΔABG ΔCGB 3. SSS A. Reflexive B. Symmetric C. Transitive D. Substitution

37 Use SAS or SSS in Proofs Write a paragraph proof. Prove: Q S

38 Answer: Use SAS or SSS in Proofs

39 Answer: Use SAS or SSS in Proofs

40 Choose the correct reason to complete the following flow proof. A. Segment Addition Postulate B. Symmetric Property C. Midpoint Theorem D. Substitution

41 Choose the correct reason to complete the following flow proof. A. Segment Addition Postulate B. Symmetric Property C. Midpoint Theorem D. Substitution

42

Unit 1: Introduction to Proof

Unit 1: Introduction to Proof Unit 1: Introduction to Proof Prove geometric theorems both formally and informally using a variety of methods. G.CO.9 Prove and apply theorems about lines and angles. Theorems include but are not restricted

More information

LESSON 2 5 CHAPTER 2 OBJECTIVES

LESSON 2 5 CHAPTER 2 OBJECTIVES LESSON 2 5 CHAPTER 2 OBJECTIVES POSTULATE a statement that describes a fundamental relationship between the basic terms of geometry. THEOREM a statement that can be proved true. PROOF a logical argument

More information

Section 5-1: Special Segments in Triangles

Section 5-1: Special Segments in Triangles Section 5-1: Special Segments in Triangles Objectives: Identify medians, altitudes, angle bisectors, and perpendicular bisectors. perpendicular bisector C median altitude Vocabulary: A B Perpendicular

More information

Over Lesson 5 3 Questions 1 & 2 Questions 3 & 4 What is the relationship between the lengths of RS and ST? What is the relationship between the length

Over Lesson 5 3 Questions 1 & 2 Questions 3 & 4 What is the relationship between the lengths of RS and ST? What is the relationship between the length Five-Minute Check (over Lesson 5 3) CCSS Then/Now New Vocabulary Key Concept: How to Write an Indirect Proof Example 1: State the Assumption for Starting an Indirect Proof Example 2: Write an Indirect

More information

Honors Geometry Term 1 Practice Final

Honors Geometry Term 1 Practice Final Name: Class: Date: ID: A Honors Geometry Term 1 Practice Final Short Answer 1. RT has endpoints R Ê Ë Á 4,2 ˆ, T Ê ËÁ 8, 3 ˆ. Find the coordinates of the midpoint, S, of RT. 5. Line p 1 has equation y

More information

Five-Minute Check (over Lesson 3 1) CCSS Then/Now Postulate 3.1: Corresponding Angles Postulate Example 1: Use Corresponding Angles Postulate

Five-Minute Check (over Lesson 3 1) CCSS Then/Now Postulate 3.1: Corresponding Angles Postulate Example 1: Use Corresponding Angles Postulate Five-Minute Check (over Lesson 3 1) CCSS Then/Now Postulate 3.1: Corresponding Angles Postulate Example 1: Use Corresponding Angles Postulate Theorems: Parallel Lines and Angle Pairs Proof: Alternate Interior

More information

Over Lesson 7 2 Determine whether the triangles are similar. The quadrilaterals are similar. Find the scale factor of the larger quadrilateral to the

Over Lesson 7 2 Determine whether the triangles are similar. The quadrilaterals are similar. Find the scale factor of the larger quadrilateral to the Five-Minute Check (over Lesson 7 2) CCSS Then/Now Postulate 7.1: Angle-Angle (AA) Similarity Example 1: Use the AA Similarity Postulate Theorems Proof: Theorem 7.2 Example 2: Use the SSS and SAS Similarity

More information

Over Lesson 2 7 Justify the statement with a property of equality or a property of congruence. Justify the statement with a property of equality or a

Over Lesson 2 7 Justify the statement with a property of equality or a property of congruence. Justify the statement with a property of equality or a Five-Minute Check (over Lesson 2 7) CCSS Then/Now Postulate 2.10: Protractor Postulate Postulate 2.11: Angle Addition Postulate Example 1: Use the Angle Addition Postulate Theorems 2.3 and 2.4 Example

More information

Find the geometric mean between 9 and 13. Find the geometric mean between

Find the geometric mean between 9 and 13. Find the geometric mean between Five-Minute Check (over Lesson 8 1) CCSS Then/Now New Vocabulary Theorem 8.4: Pythagorean Theorem Proof: Pythagorean Theorem Example 1: Find Missing Measures Using the Pythagorean Theorem Key Concept:

More information

Over Lesson 5 5 (1-3) Determine whether it is possible to form a triangle with the given lengths of sides:. 5, 7, and , 4.2, and , 6, and

Over Lesson 5 5 (1-3) Determine whether it is possible to form a triangle with the given lengths of sides:. 5, 7, and , 4.2, and , 6, and Five-Minute Check (over Lesson 5 5) CCSS Then/Now Theorems: Inequalities in Two Triangles Example 1: Use the Hinge Theorem and its Converse Proof: Hinge Theorem Example 2: Real-World Example: Use the Hinge

More information

Five-Minute Check (over Lesson 5 5) CCSS Then/Now Theorems: Inequalities in Two Triangles Example 1: Use the Hinge Theorem and its Converse Proof:

Five-Minute Check (over Lesson 5 5) CCSS Then/Now Theorems: Inequalities in Two Triangles Example 1: Use the Hinge Theorem and its Converse Proof: Five-Minute Check (over Lesson 5 5) CCSS Then/Now Theorems: Inequalities in Two Triangles Example 1: Use the Hinge Theorem and its Converse Proof: Hinge Theorem Example 2: Real-World Example: Use the Hinge

More information

ACTIVITY 15 Continued Lesson 15-2

ACTIVITY 15 Continued Lesson 15-2 Continued PLAN Pacing: 1 class period Chunking the Lesson Examples A, B Try These A B #1 2 Example C Lesson Practice TEACH Bell-Ringer Activity Read the introduction with students and remind them of the

More information

Geometry CP - Ch. 4 Review

Geometry CP - Ch. 4 Review Geometry CP - Ch. 4 Review 1. If, which of the following can you NOT conclude as being true? A. B. C. D. 2. A. B. C. D. 3. Given and, find the length of QS and TV. A. 7 B. 25 C. 8 D. 2 4. The two triangles

More information

Five-Minute Check (over Lesson 2 7) CCSS Then/Now Postulate 2.10: Protractor Postulate Postulate 2.11: Angle Addition Postulate Example 1: Use the

Five-Minute Check (over Lesson 2 7) CCSS Then/Now Postulate 2.10: Protractor Postulate Postulate 2.11: Angle Addition Postulate Example 1: Use the Five-Minute Check (over Lesson 2 7) CCSS Then/Now Postulate 2.10: Protractor Postulate Postulate 2.11: Angle Addition Postulate Example 1: Use the Angle Addition Postulate Theorems 2.3 and 2.4 Example

More information

Postulates and Theorems in Proofs

Postulates and Theorems in Proofs Postulates and Theorems in Proofs A Postulate is a statement whose truth is accepted without proof A Theorem is a statement that is proved by deductive reasoning. The Reflexive Property of Equality: a

More information

Geometry GENERAL GEOMETRY

Geometry GENERAL GEOMETRY Geometry GENERAL GEOMETRY Essential Vocabulary: point, line, plane, segment, segment bisector, midpoint, congruence I can use the distance formula to determine the area and perimeters of triangles and

More information

IMPORTANT VOCABULARY. Scalene Triangle. Triangle. SSS ASA SAS AAS sides/angles

IMPORTANT VOCABULARY. Scalene Triangle. Triangle. SSS ASA SAS AAS sides/angles 1 Pre-AP Geometry Chapter 5 Test Review Standards/Goals: C.1.f.: I can prove that two triangles are congruent by applying the SSS, SAS, ASA, and AAS congruence statements. C.1.g. I can use the principle

More information

Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1

Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1 Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1 Multiple Choice. Identify the choice that best completes the statement or answers the question. 1. Which statement(s)

More information

2.8 Proving angle relationships cont. ink.notebook. September 20, page 84 page cont. page 86. page 85. Standards. Cont.

2.8 Proving angle relationships cont. ink.notebook. September 20, page 84 page cont. page 86. page 85. Standards. Cont. 2.8 Proving angle relationships cont. ink.notebook page 84 page 83 2.8 cont. page 85 page 86 Lesson Objectives Standards Lesson Notes 2.8 Proving Angle Relationships Cont. Press the tabs to view details.

More information

Geometry. Midterm Review

Geometry. Midterm Review Geometry Midterm Review Class: Date: Geometry Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1 A plumber knows that if you shut off the water

More information

IB MYP Unit 6 Review

IB MYP Unit 6 Review Name: Date: 1. Two triangles are congruent if 1. A. corresponding angles are congruent B. corresponding sides and corresponding angles are congruent C. the angles in each triangle have a sum of 180 D.

More information

Unit 5, Lesson 4.3 Proving the Pythagorean Theorem using Similarity

Unit 5, Lesson 4.3 Proving the Pythagorean Theorem using Similarity Unit 5, Lesson 4.3 Proving the Pythagorean Theorem using Similarity Geometry includes many definitions and statements. Once a statement has been shown to be true, it is called a theorem. Theorems, like

More information

5-5 The Triangle Inequality

5-5 The Triangle Inequality Is it possible to form a triangle with the given side lengths? If not, explain why not. 1. 5 cm, 7 cm, 10 cm Yes; 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5 3. 6 m, 14 m, 10 m Yes; 6 + 14 > 10, 6 + 10 > 14,

More information

Geometry First Semester Exam Review

Geometry First Semester Exam Review Geometry First Semester Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Name three points that are collinear. a. points T, Q, and R c. points

More information

Content Standards G.CO.10 Prove theorems about triangles. G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to

Content Standards G.CO.10 Prove theorems about triangles. G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to Content Standards G.CO.10 Prove theorems about triangles. G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working

More information

Instructional Goal Terminal Objective Assessment Item Students will generate twocolumn

Instructional Goal Terminal Objective Assessment Item Students will generate twocolumn eport Two Objectives Instructional Goal Terminal Objective ssessment Item Students will generate twocolumn geometric proofs. PS Given a statement to be proven, a diagram, and a given statement student

More information

1-2 Measuring and Constructing Segments

1-2 Measuring and Constructing Segments 1-2 Measuring and Constructing Segments Warm Up Lesson Presentation Lesson Quiz Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Vocabulary coordinate midpoint

More information

2-6 Geometric Proof. Warm Up Lesson Presentation Lesson Quiz. Holt Geometry

2-6 Geometric Proof. Warm Up Lesson Presentation Lesson Quiz. Holt Geometry 2-6 Geometric Proof Warm Up Lesson Presentation Lesson Quiz Warm Up Determine whether each statement is true or false. If false, give a counterexample. 1. It two angles are complementary, then they are

More information

8-6. a: 110 b: 70 c: 48 d: a: no b: yes c: no d: yes e: no f: yes g: yes h: no

8-6. a: 110 b: 70 c: 48 d: a: no b: yes c: no d: yes e: no f: yes g: yes h: no Lesson 8.1.1 8-6. a: 110 b: 70 c: 48 d: 108 8-7. a: no b: yes c: no d: yes e: no f: yes g: yes h: no 8-8. b: The measure of an exterior angle of a triangle equals the sum of the measures of its remote

More information

Practice TEST Unit 3: Congruence

Practice TEST Unit 3: Congruence Geometry Practice Test Unit 3 ongruence (G.O.B.6 - G.O..9) Name: Date: Pd: 1) Isometric transformations preserve key characteristics of a shape. Which of the following transformations is NOT an isometry?

More information

NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST. Name: Date:

NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST. Name: Date: NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST Name: Date: Day 1 1. Determine the value of x if ΔABC is equilateral. B 7.5x 6x + 3 A Write your answer on the line. 10x 5 C What is the

More information

Geometry Triangles

Geometry Triangles 1 Geometry Triangles 2015-12-08 www.njctl.org 2 Table of Contents Click on the topic to go to that section Triangles Triangle Sum Theorem Exterior Angle Theorem Inequalities in Triangles Similar Triangles

More information

2-7 Flowchart and Paragraph Proofs

2-7 Flowchart and Paragraph Proofs 2-7 Flowchart and Paragraph Proofs Warm Up Lesson Presentation Lesson Quiz Geometry Angle Relationship Worksheet Math Warehouse Proof Quiz http://www.mathwarehouse.com/properties/p roperties-quiz.php Warm

More information

1-2 Measuring and Constructing Segments

1-2 Measuring and Constructing Segments 1-2 Measuring and Constructing Segments Lesson Presentation Lesson Quiz Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Vocabulary coordinate midpoint distance

More information

Geometry Chapter 3 & 4 Test

Geometry Chapter 3 & 4 Test Class: Date: Geometry Chapter 3 & 4 Test Use the diagram to find the following. 1. What are three pairs of corresponding angles? A. angles 1 & 2, 3 & 8, and 4 & 7 C. angles 1 & 7, 8 & 6, and 2 & 4 B. angles

More information

Chapter 03 Test. 1 Complete the congruence statement. A B C D. 2 Complete the congruence statement. A B C D

Chapter 03 Test. 1 Complete the congruence statement. A B C D. 2 Complete the congruence statement. A B C D hapter 03 Test Name: ate: 1 omplete the congruence statement. 2 omplete the congruence statement. 3 If, which of the following can you NOT conclude as being true? opyright 2005-2006 by Pearson Education

More information

Homework 10: p.147: 17-41, 45

Homework 10: p.147: 17-41, 45 2-4B: Writing Proofs Homework 10: p.147: 17-41, 45 Learning Objectives: Analyze figures to identify and use postulates about points, lines and planes Analyze and construct viable arguments in several proof

More information

1) If AB is congruent to AC, then B is congruent to C.

1) If AB is congruent to AC, then B is congruent to C. 233 1) If is congruent to, then is congruent to. Proof of 1). 1) ssume ". (We must prove that ".) 2) ", because the identity is a rigid motion that moves to. 3) Therefore, Δ " Δ by the xiom. (The correspondence

More information

Which statement is true about parallelogram FGHJ and parallelogram F ''G''H''J ''?

Which statement is true about parallelogram FGHJ and parallelogram F ''G''H''J ''? Unit 2 Review 1. Parallelogram FGHJ was translated 3 units down to form parallelogram F 'G'H'J '. Parallelogram F 'G'H'J ' was then rotated 90 counterclockwise about point G' to obtain parallelogram F

More information

Chapter Review #1-3. Choose the best answer.

Chapter Review #1-3. Choose the best answer. Chapter Review #1- Choose the best answer. 1. Which statement is NOT true? A Parallel lines do not intersect. B A segment has exactly two endpoints. C Two planes that do not intersect are always skew.

More information

Properties of Isosceles and Equilateral Triangles

Properties of Isosceles and Equilateral Triangles Properties of Isosceles and Equilateral Triangles In an isosceles triangle, the sides and the angles of the triangle are classified by their position in relation to the triangle s congruent sides. Leg

More information

Name: Date: Period: 1. In the diagram below,. [G.CO.6] 2. The diagram below shows a pair of congruent triangles, with and. [G.CO.

Name: Date: Period: 1. In the diagram below,. [G.CO.6] 2. The diagram below shows a pair of congruent triangles, with and. [G.CO. Name: Date: Period: Directions: Read each question carefully and choose the best answer for each question. You must show LL of your work to receive credit. 1. In the diagram below,. [G.CO.6] Which statement

More information

Pythagorean Theorem a= 6.4, b = 12, c = a = 2.1, b = 7.2, c = 7.5

Pythagorean Theorem a= 6.4, b = 12, c = a = 2.1, b = 7.2, c = 7.5 Pythagorean Theorem Do the following lengths form a right triangle? 1. 2. 3. 4. 5. a= 6.4, b = 12, c = 12.2 6. a = 2.1, b = 7.2, c = 7.5 Find each missing length to the nearest tenth. 1. 2. 3. 1 Find the

More information

Midterm Study Guide Assessment. Question 1. Find the angle measure. (28x + 14) (16x + 62) The measure of the angles are. 11/30/2018 Print Assignment

Midterm Study Guide Assessment. Question 1. Find the angle measure. (28x + 14) (16x + 62) The measure of the angles are. 11/30/2018 Print Assignment Question 1. Find the angle measure. (28x + 14) (16x + 62) The measure of the angles are. https://my.hrw.com/wwtb2/viewer/printall_vs5.html?sf2tt3dnj49xcldd29v4qfjhw0nq0ker6b1uuwkuupca0a5fsymn1tdn7y3prlf19pv779ludnoev4cldd29v4

More information

2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain.

2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain. 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain. 3) Explain why a four-legged

More information

G.1.f.: I can evaluate expressions and solve equations containing nth roots or rational exponents. IMPORTANT VOCABULARY. Pythagorean Theorem

G.1.f.: I can evaluate expressions and solve equations containing nth roots or rational exponents. IMPORTANT VOCABULARY. Pythagorean Theorem Pre-AP Geometry Standards/Goals: C.1.f.: I can prove that two right triangles are congruent by applying the LA, LL, HL, and HA congruence statements. o I can prove right triangles are similar to one another.

More information

Geometry - Chapter 2 Earn-A-Try Test

Geometry - Chapter 2 Earn-A-Try Test Name: Geometry - Chapter 2 Earn-A-Try Test Multiple Choice Identify the choice that best completes the statement or answers the question. Use CAPITAL letters only!! Ex: A,B,C,D; Not a,b,c,d. 1. Write a

More information

Geometry Study Guide. Name: Class: Date: Matching

Geometry Study Guide. Name: Class: Date: Matching Name: Class: Date: ID: A Geometry Study Guide Matching Match each vocabulary term with its definition. a. conjecture e. biconditional statement b. inductive reasoning f. hypothesis c. deductive reasoning

More information

UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).

UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). EOCT Practice Items 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B'

More information

ALLEN PARK HIGH SCHOOL F i r s t S e m e s t e r R e v i e w

ALLEN PARK HIGH SCHOOL F i r s t S e m e s t e r R e v i e w ALLEN PARK HIGH SCHOOL i r s t S e m e s t e r R e v i e w G EOMERY APHS/MAH Winter 2010 DIRECIONS his section of test is 68 items, which you will work in this booklet. Mark the correct answer as directed

More information

NAME DATE PERIOD. Inductive Reasoning and Conjecture. Make a conjecture based on the given information. Draw a figure to illustrate your conjecture.

NAME DATE PERIOD. Inductive Reasoning and Conjecture. Make a conjecture based on the given information. Draw a figure to illustrate your conjecture. 2-1 NAME DATE PERIOD Skills Practice Inductive Reasoning and Conjecture Make a conjecture about the next item in each sequence. 1. 2. 4, 1, 2, 5, 8 3. 6, 1 1, 5, 9 2 2,4 4. 2, 4, 8, 16, 32 Make a conjecture

More information

Triangle Geometry. Often we can use one letter (capitalised) to name an angle.

Triangle Geometry. Often we can use one letter (capitalised) to name an angle. 1) Naming angles Triangle Geometry Often we can use one letter (capitalised) to name an angle. A C B When more than two lines meet at a vertex, then we must use three letters to name an angle. Q X P T

More information

8-6. a: 110 b: 70 c: 48 d: a: no b: yes c: no d: yes e: no f: yes g: yes h: no

8-6. a: 110 b: 70 c: 48 d: a: no b: yes c: no d: yes e: no f: yes g: yes h: no Lesson 8.1.1 8-6. a: 110 b: 70 c: 48 d: 108 8-7. a: no b: yes c: no d: yes e: no f: yes g: yes h: no 8-8. b: The measure of an exterior angle of a triangle equals the sum of the measures of its remote

More information

5.3 It s All In Your Head A Solidify Understanding Task

5.3 It s All In Your Head A Solidify Understanding Task 16 5.3 It s All In Your Head A Solidify Understanding Task In the previous task you were asked to justify some claims by writing paragraphs explaining how various figures were constructed and how those

More information

2-1 Using Inductive Reasoning to Make Conjectures

2-1 Using Inductive Reasoning to Make Conjectures CHAPTER 2 Chapter Review 2-1 Using Inductive Reasoning to Make Conjectures Find the next term in each pattern. 1. 6, 12, 18,... 2. January, April, July,... 3. The table shows the score on a reaction time

More information

Honors Geometry Semester Review Packet

Honors Geometry Semester Review Packet Honors Geometry Semester Review Packet 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary angles linear

More information

Geometry Midterm REVIEW

Geometry Midterm REVIEW Name: Class: Date: ID: A Geometry Midterm REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given LM = MP and L, M, and P are not collinear. Draw

More information

10-3 Arcs and Chords. ALGEBRA Find the value of x.

10-3 Arcs and Chords. ALGEBRA Find the value of x. ALGEBRA Find the value of x. 1. Arc ST is a minor arc, so m(arc ST) is equal to the measure of its related central angle or 93. and are congruent chords, so the corresponding arcs RS and ST are congruent.

More information

Lesson. Warm Up deductive 2. D. 3. I will go to the store; Law of Detachment. Lesson Practice 31

Lesson. Warm Up deductive 2. D. 3. I will go to the store; Law of Detachment. Lesson Practice 31 Warm Up 1. deductive 2. D b. a and b intersect 1 and 2 are supplementary 2 and 3 are supplementary 3. I will go to the store; Law of Detachment Lesson Practice a. 1. 1 and 2 are. 2. 1 and 3 are. 3. m 1

More information

5-1 Perpendicular and Angle Bisectors

5-1 Perpendicular and Angle Bisectors 5-1 Perpendicular and Angle Bisectors Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Construct each of the following. 1. A perpendicular bisector. 2. An angle bisector. 3. Find the midpoint and

More information

Find the next item in the pattern below. The red square moves in the counterclockwise direction. The next figure is.

Find the next item in the pattern below. The red square moves in the counterclockwise direction. The next figure is. CHAPTER 2 Study Guide: Review Organizer Objective: Help students organize and review key concepts and skills presented in Chapter 2. Online Edition Multilingual Glossary Countdown Week 4 Vocabulary biconditional

More information

7. m JHI = ( ) and m GHI = ( ) and m JHG = 65. Find m JHI and m GHI.

7. m JHI = ( ) and m GHI = ( ) and m JHG = 65. Find m JHI and m GHI. 1. Name three points in the diagram that are not collinear. 2. If RS = 44 and QS = 68, find QR. 3. R, S, and T are collinear. S is between R and T. RS = 2w + 1, ST = w 1, and RT = 18. Use the Segment Addition

More information

ANSWERS STUDY GUIDE FOR THE FINAL EXAM CHAPTER 1

ANSWERS STUDY GUIDE FOR THE FINAL EXAM CHAPTER 1 ANSWERS STUDY GUIDE FOR THE FINAL EXAM CHAPTER 1 N W A S Use the diagram to answer the following questions #1-3. 1. Give two other names for. Sample answer: PN O D P d F a. Give two other names for plane.

More information

9-7. a: Solutions vary. Possible solution shown at right. b: Answers vary. Assuming there are no hidden cubes, V = 11 units 3.

9-7. a: Solutions vary. Possible solution shown at right. b: Answers vary. Assuming there are no hidden cubes, V = 11 units 3. Lesson 9.1.1 9-7. a: Solutions vary. Possible solution shown at right. b: Answers vary. Assuming there are no hidden cubes, V = 11 units 0 0 1 1 1 1 9-8. a: 4 5 b: 196:1 c: 9:1 9-9. Since the perimeter

More information

Name Geometry Common Core Regents Review Packet - 3. Topic 1 : Equation of a circle

Name Geometry Common Core Regents Review Packet - 3. Topic 1 : Equation of a circle Name Geometry Common Core Regents Review Packet - 3 Topic 1 : Equation of a circle Equation with center (0,0) and radius r Equation with center (h,k) and radius r ( ) ( ) 1. The endpoints of a diameter

More information

Page 1 of 8 Name: 1. Write in symbolic form the inverse of ~p q. 1. ~q p 2. q ~ p 3. p q 4. p ~ q 2. In symbolic form, write the contrapositive of p ~q. 1. q ~ p 2. ~p ~q 3. ~p q 4. ~q p 3. Figure 1 In

More information

Unit 5: Congruency. Part 1 of 3: Intro to Congruency & Proof Pieces. Lessons 5-1 through 5-4

Unit 5: Congruency. Part 1 of 3: Intro to Congruency & Proof Pieces. Lessons 5-1 through 5-4 Name: Geometry Period Unit 5: Congruency Part 1 of 3: Intro to Congruency & Proof Pieces Lessons 5-1 through 5-4 In this unit you must bring the following materials with you to class every day: Please

More information

So, PQ is about 3.32 units long Arcs and Chords. ALGEBRA Find the value of x.

So, PQ is about 3.32 units long Arcs and Chords. ALGEBRA Find the value of x. ALGEBRA Find the value of x. 1. Arc ST is a minor arc, so m(arc ST) is equal to the measure of its related central angle or 93. and are congruent chords, so the corresponding arcs RS and ST are congruent.

More information

Integrated Math 3 Math 3 Course Description:

Integrated Math 3 Math 3 Course Description: Course Description: Integrated Math 3 Math 3 Course Description: Integrated strands include algebra, functions, geometry, trigonometry, statistics, probability and discrete math. Scope and sequence includes

More information

Chapter 2. Reasoning and Proof

Chapter 2. Reasoning and Proof Chapter 2 Reasoning and Proof 2.1 Use Inductive Reasoning Objective: Describe patterns and use deductive reasoning. Essential Question: How do you use inductive reasoning in mathematics? Common Core: CC.9-12.G.CO.9

More information

Parallel and Perpendicular Lines

Parallel and Perpendicular Lines Cumulative Test Choose the best answer. 1. Which statement is NOT true? A Parallel lines do not intersect. B A segment has exactly two endpoints. C Two planes that do not intersect are always skew. D A

More information

Geometry AIR Test. Mar 14-3:07 PM. coordinate/algebraic proofs, parallel and perpendicular lines, distance formula, midpoint formula.

Geometry AIR Test. Mar 14-3:07 PM. coordinate/algebraic proofs, parallel and perpendicular lines, distance formula, midpoint formula. Geometry AIR Test Mar 14-3:07 PM Congruence and Proof 33-39% coordinate/algebraic proofs, parallel and perpendicular lines, distance formula, midpoint formula. missing sides on triangles (trig ratios,

More information

UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).

UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B' B' C' AB BC A' B' D'

More information

End of Course Review

End of Course Review End of Course Review Geometry AIR Test Mar 14 3:07 PM Test blueprint with important areas: Congruence and Proof 33 39% Transformations, triangles (including ASA, SAS, SSS and CPCTC), proofs, coordinate/algebraic

More information

Geometer: CPM Chapters 1-6 Period: DEAL. 7) Name the transformation(s) that are not isometric. Justify your answer.

Geometer: CPM Chapters 1-6 Period: DEAL. 7) Name the transformation(s) that are not isometric. Justify your answer. Semester 1 Closure Geometer: CPM Chapters 1-6 Period: DEAL Take time to review the notes we have taken in class so far and previous closure packets. Look for concepts you feel very comfortable with and

More information

Geometry Midterm Exam Review 3. Square BERT is transformed to create the image B E R T, as shown.

Geometry Midterm Exam Review 3. Square BERT is transformed to create the image B E R T, as shown. 1. Reflect FOXY across line y = x. 3. Square BERT is transformed to create the image B E R T, as shown. 2. Parallelogram SHAQ is shown. Point E is the midpoint of segment SH. Point F is the midpoint of

More information

Using Inductive and Deductive Reasoning

Using Inductive and Deductive Reasoning Big Idea 1 CHAPTER SUMMARY BIG IDEAS Using Inductive and Deductive Reasoning For Your Notebook When you make a conjecture based on a pattern, you use inductive reasoning. You use deductive reasoning to

More information

Name Class Date. Additional Vocabulary Support. Reasoning in Algebra and Geometry

Name Class Date. Additional Vocabulary Support. Reasoning in Algebra and Geometry Additional Vocabulary Support Concept List Addition Property of Equality Division Property of Equality Reflexive Property of Equality Subtraction Property of Equality Transitive Property of Equality Distributive

More information

Geometry Unit 5 Review Show all work and follow the criteria for credit.

Geometry Unit 5 Review Show all work and follow the criteria for credit. ompetency 1: Identify ongruence For questions 1 5, decide which congruence postulate, if any, you can use to prove that the given triangles are congruent. rite the congruence statement and identify the

More information

Chapter 2. Reasoning and Proof

Chapter 2. Reasoning and Proof Chapter 2 Reasoning and Proof 2.1 Use Inductive Reasoning Objective: Describe patterns and use deductive reasoning. Essential Question: How do you use inductive reasoning in mathematics? Common Core: CC.9-12.G.CO.9

More information

Cumulative Test. 101 Holt Geometry. Name Date Class

Cumulative Test. 101 Holt Geometry. Name Date Class Choose the best answer. 1. Which of PQ and QR contains P? A PQ only B QR only C Both D Neither. K is between J and L. JK 3x, and KL x 1. If JL 16, what is JK? F 7 H 9 G 8 J 13 3. SU bisects RST. If mrst

More information

Chapter Test. Chapter Tests LM 5 4, }} MO 5 14, } LN Answers. In Exercises 4 6, use the diagram. Geometry Benchmark Tests

Chapter Test. Chapter Tests LM 5 4, }} MO 5 14, } LN Answers. In Exercises 4 6, use the diagram. Geometry Benchmark Tests Chapter Test For use after Chapter. Which of the following is not an undefined term? A. Point B. Plane C. Line D. Ray. Which of the following is an undefined term? A. Line B. Ray C. Segment D. Intersection

More information

Distance. Warm Ups. Learning Objectives I can find the distance between two points. Football Problem: Bailey. Watson

Distance. Warm Ups. Learning Objectives I can find the distance between two points. Football Problem: Bailey. Watson Distance Warm Ups Learning Objectives I can find the distance between two points. Football Problem: Bailey Watson. Find the distance between the points (, ) and (4, 5). + 4 = c 9 + 6 = c 5 = c 5 = c. Using

More information

2/11/16 Review for Proofs Quiz

2/11/16 Review for Proofs Quiz 2/11/16 Review for Proofs Quiz EQ:Name some of the most common properties, theorems, and postulates used when performing proofs. MCC9 12.G.CO.9 Prove theorems about lines and angles. Theorems include:

More information

Chapter 2 Segment Measurement and Coordinate Graphing

Chapter 2 Segment Measurement and Coordinate Graphing Geometry Concepts Chapter 2 Segment Measurement and Coordinate Graphing 2.2 Find length segments (1.3) 2.3 Compare lengths of segments (1.3) 2.3 Find midpoints of segments (1.7) 2.5 Calculate coordinates

More information

2.6 algebraic proofs. September 13, algebraic proofs ink.notebook. Page 71. Page 72 Page 70. Page 73. Standards. 2.

2.6 algebraic proofs. September 13, algebraic proofs ink.notebook. Page 71. Page 72 Page 70. Page 73. Standards. 2. 2.6 algebraic proofs ink.notebook September 13, 2017 Page 71 Page 72 Page 70 2.6 algebraic proofs Page 73 Lesson Objectives Standards Lesson Notes 2.6 Algebraic Proofs Press the tabs to view details. 1

More information

HONORS GEOMETRY CHAPTER 2 WORKBOOK

HONORS GEOMETRY CHAPTER 2 WORKBOOK HONORS GEOMETRY CHAPTER 2 WORKBOOK FALL 2016 Chapter 2 Miscellaneous: The Structure of Geometry Vocabulary Definition Example Elements: 1. Deductive Structure Postulate (axiom) Example: Definitions Reversed:

More information

North Carolina Math 2 Transition Edition Unit 4 Assessment: Similarity and Congruence

North Carolina Math 2 Transition Edition Unit 4 Assessment: Similarity and Congruence Name: Class: _ Date: _ North Carolina Math 2 Transition Edition Unit 4 Assessment: Similarity and Congruence Multiple Choice Identify the choice that best completes the statement or answers the question.

More information

Unit 5, Day 1: Ratio s/proportions & Similar Polygons

Unit 5, Day 1: Ratio s/proportions & Similar Polygons Date Period Unit 5, Da 1: Ratio s/proportions & Similar Polgons 1. If a) 5 7, complete each statement below. b) + 7 c) d) 7 2. Solve each proportion below. Verif our answer is correct. a) 9 12 b) 24 5

More information

Investigating Similar Triangles and Understanding Proportionality: Lesson Plan

Investigating Similar Triangles and Understanding Proportionality: Lesson Plan Investigating Similar Triangles and Understanding Proportionality: Lesson Plan Purpose of the lesson: This lesson is designed to help students to discover the properties of similar triangles. They will

More information

Name: 2015 Midterm Review Period: Date:

Name: 2015 Midterm Review Period: Date: GEOMETRY Name: 2015 Midterm Review Period: Date: To be prepared for your midterm, you will need to PRACTICE PROBLEMS and STUDY TERMS from the following chapters. Use this guide to help you practice. UNIT

More information

C XZ if C XY > C YZ. Answers for the lesson Apply Properties of Chords. AC } DB therefore you can t show C BC > C CD. 4x x 1 8.

C XZ if C XY > C YZ. Answers for the lesson Apply Properties of Chords. AC } DB therefore you can t show C BC > C CD. 4x x 1 8. LESSON 10.3 Answers for the lesson Apply Properties of Chords Copyright Houghton Mifflin Harcourt Publishing Company. All rights reserved. Skill Practice 1. Sample answer: Point Y bisects C XZ if C XY

More information

Chapter 2 Practice Test

Chapter 2 Practice Test Name: Class: Date: ID: A Chapter 2 Practice Test 1. What is a counterexample for the conjecture? Conjecture: Any number that is divisible by 4 is also divisible by 8. 2. What is the conclusion of the following

More information

2.4 Algebraic and Congruence Properties

2.4 Algebraic and Congruence Properties 2.4 Algebraic and Congruence Properties Learning Objectives Understand basic properties of equality and congruence. Solve equations and justify each step in the solution. Use a 2-column format to prove

More information

4) Find the value of the variable and YZ if Y is between X and Z. XY = 2c +1, YZ = 6c, XZ = 9c 1 6(2) 12 YZ YZ

4) Find the value of the variable and YZ if Y is between X and Z. XY = 2c +1, YZ = 6c, XZ = 9c 1 6(2) 12 YZ YZ Pre-AP Geometry 1 st Semester Exam Study Guide 1) Name the intersection of plane DAG and plane ABD. (left side and back) AD ) Name the intersection of HI and FJ E 3) Describe the relationship between the

More information

Reasoning and Proof Unit

Reasoning and Proof Unit Reasoning and Proof Unit 1 2 2 Conditional Statements Conditional Statement if, then statement the if part is hypothesis the then part is conclusion Conditional Statement How? if, then Example If an angle

More information

Content Descriptions Based on the state-mandated content standards. Analytic Geometry

Content Descriptions Based on the state-mandated content standards. Analytic Geometry Content Descriptions Based on the state-mandated content standards Analytic Geometry Introduction The State Board of Education is required by Georgia law (A+ Educational Reform Act of 2000, O.C.G.A. 20-2-281)

More information

Assignment Assignment for Lesson 6.1

Assignment Assignment for Lesson 6.1 Assignment Assignment for Lesson.1 Name Date Constructing Congruent Triangles or Not Constructing Triangles In each exercise, do the following. a. Use the given information to construct a triangle. b.

More information

Attendance Problems 1. Write a conditional from the sentence An isosceles triangle has two congruent sides.

Attendance Problems 1. Write a conditional from the sentence An isosceles triangle has two congruent sides. Page 1! of 11! Attendance Problems 1. Write a conditional from the sentence An isosceles triangle has two congruent sides. 2. Write the contrapositive of the conditional If it is Tuesday, then John has

More information

+ 10 then give the value

+ 10 then give the value 1. Match each vocabulary word to the picture. A. Linear Pair B. Vertical Angles P1 C. Angle Bisector D. Parallel Lines E. Orthocenter F. Centroid For questions 3 4 use the diagram below. Y Z X U W V A

More information