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GEOMETRY Lesson 15 NYS COMMON CORE MATHEMATICS CURRICULUM Name:__________________________________ M2 Date:_______________ LESSON 15: THE AA CRITERION FOR SIMILAR TRIANGLES IMPORTANT NOTATION: IF 𝑨 AND 𝑩 ARE SIMILAR, WE WRITE 𝑨~𝑩 WHERE “~” DENOTES SIMILARITY. THEOREM: Two triangles with two pairs of equal corresponding angles are similar. This is known as the AA criterion for similarity. We know that similar figures have equal corresponding angle measures. We also know if two angles in one triangle are equal in measure to two corresponding angles in another triangle, then it must be the case that the third corresponding angles in each triangle must also be of equal measure. ex. 40⁰ 40⁰ 35⁰ 0⁰ 35⁰ 0⁰ In Exercises 1–4, practice using the AA criterion to determine if two triangles are similar and then determine unknown side lengths and/or angle measures of the triangles. 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° 78.46° 7 Lesson 15: Date: 57.12° The Angle-Angle (AA) Criterion for Two Triangles to be Similar 4/1/16 © 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 229 2. Are the triangles shown below similar? Explain. If the triangles are similar, identify any missing angle and side length measures. 3. The triangles shown below are similar. Use what you know about similar triangles to find the missing side lengths 𝒙 and 𝒚. 4. The triangles shown below are similar. Write an explanation to a student, Claudia, of how to find the lengths of 𝒙 and 𝒚. Lesson 15: Date: The Angle-Angle (AA) Criterion for Two Triangles to be Similar 4/1/16 © 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 230 Name Date Geometry L.15 AA Similarity HW Period:______________ 1. a. b. 2. a. b. Lesson 15: Date: The Angle-Angle (AA) Criterion for Two Triangles to be Similar 4/1/16 © 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 231 3. a. b. c. d. Lesson 15: Date: The Angle-Angle (AA) Criterion for Two Triangles to be Similar 4/1/16 © 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 232