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NAME: Lesson 6: Defining and Applying Similarity 6/*5tSIMILARITY, CONGRUENCE, AND PROOFS Lesson 6: Defining and Applying Similarity Assessment 5. Are the two triangles !Unit!2!Geometry!Triangle!Similarity!Quiz! similar? Why or why not? Assessment ! C 1.!! 5. Are the two triangles similar? Why or why not? A ! C ! B A ! B ! E ! ! E D ! ! a. Yes, they are similar because of the AA Similarity Statement. D ! ! b. Yes, Yes, they they are are similar similar because because of of the the AA ASASimilarity Congruence Statement. a. Statement. ! No, they similar because congruence is not preserved. b.c. Yes, they are are not similar because of the ASA Congruence Statement. ! ! d. No, It cannot be not determined if the triangles are similar. c. they are similar because congruence is not preserved. ! ! d. It cannot be determined if the triangles are similar. ! 2.!! 6. Are the two triangles similar? Why or why not? ! C 6. Are the two triangles similar? Why or why not? ! B ! C ! B ! F D ! F ! D ! E ! ! E ! A ! a. Yes, they are A similar because of the AA Similarity Statement. ! ! NAME: b. Yes, Yes, they they are are similar similar because because of of the the AA ASASimilarity Congruence Statement. a. Statement. ! 6/*5tSIMILARITY, CONGRUENCE, AND PROOFS No, they not similar because congruence is not preserved. ! b.c. Yes, they are are similar because of the ASA Congruence Statement. ! Lesson 6: Defining and Applying Similarity d. No, It cannot be not determined if the triangles are similar. c. they are similar because congruence is not preserved. ! Assessment ! d. It cannot be determined if the triangles are similar. 3.!! 7. ABC has undergone a series of similarity transformations to produce EFG . Which of the ! following statements is always true? ! a. The angles of EFG are proportional to the angles of ABC . ! continued ! b. The angles of EFG are the same as the angles of ABC . continued ! ! c. The sides of EFG increase proportionally to the sides of ABC . CCGPS Analytic Geometry Teacher U1-367 © Walch Education Resource ! U1-367 d. The sides of EFG decrease proportionally to the sides of ABC . ! © Walch Education CCGPS Analytic Geometry Teacher Resource ! 8. Identify the similar triangles. E 9. Identify the similar triangles. Find x. 4.!! C ! D x ! 6 2 9 ! A NAME: ! E B !6/*5tSIMILARITY, CONGRUENCE, AND PROOFS F ! Lesson 7: Proving Similarity 1 ! x = a. △ ABC ∼△ FED ; x = 3 c. △ ABC ∼△ FED ; ! Assessment 3 ! 1 ! Progress b. Assessment △ ABC ∼△ DEF ; x = 3 d. △ ABC ∼△ DEF ; x = ! Circle the letter of the best answer. 3 ! 5.! 1. Which statement would justify △ ABC ∼△ DEF ? continued ! ! A ! U1-368 D CCGPS Analytic Geometry Teacher Resource © Walch Education 14 ! 7 ! E ! B 5 ! ! 6 ! 10 F ! ! 12 ! ! ! C ! ! ! a. Angle-Angle (AA) Similarity Statement ! b. Side-Angle-Side (SAS) Similarity Statement ! ! c. Side-Side-Side (SSS) Similarity Statement ! d. It is not possible to determine if △ ABC ∼△ DEF . ! ! ! ! ! ! ! ! ! ! ! ! !! ! continued d. It is not possible to determine if △ ABC ∼△ DEF . 3. Which statement would justify △ ABC ∼△ DEF ? 6.! ! 15 A B ! ! 10 D E ! ! ! 12 ! 7 ! ! ! F C ! ! a. Angle-Angle (AA) Similarity Statement NAME: ! b. Side-Angle-Side (SAS) Similarity ! 6/*5tSIMILARITY, CONGRUENCE, AND Statement PROOFS ! continued c. Side-Side-Side Lesson 7: Proving Similarity(SSS) Similarity Statement ! d. It is not possible to determine if △ ABC ∼△ DEF . Assessment ! U1-457 ! © Walch Education CCGPS Analytic Geometry Teacher Resource 4. △ ABF ∼△ ACE . What is the length of CB ? 7.!!!! ! C ! x ! B ! ! ! 12 ! ! A ! 9 5.4 E F ! ! a. 7.2 units ! ! b. 4.05 units ! c. 20 units ! ! d. There is not enough information to determine the length of CB . ! ! ! ! 5. △ ABD ∼△ECD . What is the length of CD ? ! B ! ! C ! 30 ! x ! ! ! ! D 6 18 A E a. 90 units d. There is not enough information to determine the length of CB . 8.!5. △ ABD ∼△ECD . What is the length of CD ? ! B ! ! C ! 30 ! x ! ! ! ! 6 18 A E ! ! a. 90 units ! ! NAME: b. 7.5 units ! 6/*5tSIMILARITY, CONGRUENCE, AND PROOFS c. 22.5 units ! Lesson 7: Proving Similarity ! d. There is not enough information to determine the length of CD . ! ! 2. Which statement would justify △ ABC ∼△ DEF ? 9.! E ! ! ! ! U1-458 ! CCGPS Analytic Geometry Teacher Resource ! ! ! ! 15 B ! ! ! 5 ! ! ! ! A ! C 3 F 9 ! ! a. Angle-Angle (AA) Similarity Statement ! b. Side-Angle-Side (SAS) Similarity Statement ! ! c. Side-Side-Side (SSS) Similarity Statement ! d. It is not possible to determine if △ ABC ∼△ DEF . ! ! ! 3. Which statement would justify △ ABC ∼△ DEF ? ! 15 A B ! ! D 12 D Assessment continued © Walch Education D 10 E Read the scenario below and answer the questions that follow. 11. Suppose you are standing near a building and you want to know its height. The building casts a 10.!!!! 70-foot shadow. You cast a 4-foot shadow. a. If you are 5 feet 6 inches tall, how tall is the building? b. A nearby fence post is 3 feet tall. What is the approximate length of its shadow? c. Explain how the Angle-Angle (AA) Similarity Statement helps you solve this problem. U1-369 © Walch Education CCGPS Analytic Geometry Teacher Resource