In this lesson, students use the Angle-Side-Angle Triangle Congruence Theorem as the basis for proving the Angle-Angle Triangle Similarity Theorem. Students make use of the structure of the Angle-Side-Angle Triangle Congruence Theorem along with their understanding of dilations to prove that two triangles with 2 pairs of corresponding congruent angles must be similar (MP7).

Students then make use of the Triangle Sum Theorem along with the Angle-Angle Triangle Similarity Theorem to determine other angle conditions that could be used to determine whether two triangles are similar.

Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.