Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 8, Part B:
Similar Triangles

In This Part: The Mirror Trick | Similarity Tests | Measuring with Shadows

Problem B2

For each pair of angles given below, sketch at least three different triangles that have these two angle measures. What do you notice? Note 6

 a. 90° and 60° b. 45° and 45° c. 120° and 30° d. 80° and 40°

In Part A, we outlined an argument that if two triangles have all three pairs of sides in proportion, the triangles must be similar. This is the SSS similarity test.

There are two other similarity tests:

 • AAA similarity: If two triangles have corresponding angles that are congruent, then the triangles are similar. Because the sum of the angles in a triangle must be 180°, you really only need to know that two pairs of corresponding angles are congruent to know the triangles are similar. • SAS similarity: If two triangles have two pairs of sides that are proportional and the included angles are congruent, then the triangles are similar.

 Session 8: Index | Notes | Solutions | Video