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Name ______________________________ Angle-Angle Triangle Similarity Module 2 Lesson 15 Learning Target: I can use the angle-angle criterion for two triangles to be similar. Opening Exercise If βQRS ~ βXYZ, identify the pairs of congruent angles and write 3 proportions using pairs of corresponding sides. Angle-Angle (AA) Triangle Similarity 1. Explain why the triangles are similar and write a similarity statement. 2. Explain why the triangles are similar and write a similarity statement. 3. Given: πΈπ΅ β₯ π΄π΅ and π·πΆ β₯ π΄πΆ. Prove βABE ~ βACD, and then find CD. 4. The triangles shown below are similar. Use what you know about similar triangles to find the missing side lengths π₯ and π¦. 5. The triangles shown below are similar. Write an explanation to a student, Claudia, of how to find the lengths of π₯ and π¦. Name ______________________________ Angle-Angle Triangle Similarity Module 2 Lesson 15 Problem Set 1. Are the triangles shown below similar? Explain. If the triangles are similar, identify any missing angle and side length measures. 28 20 3 8 6 44.42° 57.12° 7 78.46° 57.12° 2. Are the triangles shown below similar? Explain. If the triangles are similar, identify any missing angle and side length measures. 3. In the figure below, β³ πΏππ~ β³ πππΏ. a. Classify β³ πΏππ based on what you know about similar triangles and justify your reasoning. b. If πβ π = 20°, find the remaining angles in the diagram. Μ Μ Μ Μ , Μ Μ Μ Μ 4. In the diagram below of βππ π, Q is a point on Μ Μ Μ Μ ππ , S is a point on ππ ππ is drawn, and β π ππ β β π ππ. Which reason justifies the conclusion that βππ π~βππ π? 5. In the diagram of βπ΄π΅πΆ and βπΈπ·πΆ below, Μ Μ Μ Μ π΄πΈ and Μ Μ Μ Μ π΅π· intersect at C, and β πΆπ΄π΅ β β πΆπΈπ·. Which method can be used to show that βπ΄π΅πΆ must be similar to βπΈπ·πΆ? 6. The diagram below shows βπ΄π΅πΆ, with Μ Μ Μ Μ Μ Μ π΄πΈπ΅ , Μ Μ Μ Μ Μ Μ π΄π·πΆ , and β π΄πΆπ΅ β β π΄πΈπ·. Prove that βπ΄π΅πΆ is similar to βπ΄π·πΈ. 7. In the diagram below, , , , and . Prove that . 8. In the accompanying diagram, . and and intersect at point T. Prove that Name ______________________________ Angle-Angle Triangle Similarity Given the diagram below and Μ Μ Μ Μ π·πΈ β₯ Μ Μ Μ Μ πΎπΏ, find πΉπΈ and πΉπΏ. Module 2 Lesson 15 Exit Ticket