Lesson 3: 7-3: Similar Triangles - AA Similarity

1. How many pairs of corresponding angles need to be congruent in order to prove the two triangles are similar?
2. How can you use the AA similarity criterion to solve problems with similar triangles?

Similar Triangles

G.SRT.3
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
G.SRT.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Triangles can be proved similar without knowing the measures of every angle and side. The AA similarity criterion, stated as the AA Similarity Postulate, establishes that two triangles are similar if two pairs of their angles are congruent. The properties of similar triangles can be used in indirect measurement, which can be useful in solving real-world problems.

Julian wants to draw a similar version of his lacrosse club's logo on a poster. He first draws a line at the bottom of the poster. Next, he uses a cutout of the original triangle to copy the two bottom angles. Finally, he extends the non-common sides of the two angles to create a similar triangle.

It's important to note that when given two angles in each triangle, it may be necessary to find the third angle in each triangle before checking for AA similarity.

Students approaching grade level can be given practice problems in small groups to work with other students or directly with the teacher.
Students beyond grade level can make deeper connections by justifying why knowing two angle pairs are congruent is enough to know that the two triangles are similar.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.