# The Angle-Angle (AA) Criterion for Two Triangles to Be Similar

### New York State Common Core Math Geometry, Module 2, Lesson 15

Worksheets for Geometry, Module 2, Lesson 15

Student Outcomes

• Students prove the angle-angle criterion for two triangles to be similar and use it to solve triangle problems.

The Angle-Angle (AA) Criterion for Two Triangles to Be Similar

Classwork

Exercises

1. Draw two triangles of different sizes with two pairs of equal angles. Then, measure the lengths of the corresponding sides to verify that the ratio of their lengths is proportional. Use a ruler, compass, or protractor, as necessary.
2. Are the triangles you drew in Exercise 1 similar? Explain.
3. Why is it that you only need to construct triangles where two pairs of angles are equal but not three?
4. Why were the ratios of the corresponding sides proportional?
1. Do you think that what you observed will be true when you construct a pair of triangles with two pairs of equal angles? Explain.
2. Draw another two triangles of different sizes with two pairs of equal angles. Then, measure the lengths of the corresponding sides to verify that the ratio of their lengths is proportional. Use a ruler, compass, or protractor, as necessary.
3. Are the triangles shown below similar? Explain. If the triangles are similar, identify any missing angle and sidelength measures.
4. Are the triangles shown below similar? Explain. If the triangles are similar, identify any missing angle and sidelength measures.
5. The triangles shown below are similar. Use what you know about similar triangles to find the missing side lengths 𝑥 and 𝑦.
6. The triangles shown below are similar. Write an explanation to a student, Claudia, of how to find the lengths of 𝑥 and 𝑦.

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