Triangle Similarity Theorems

Front

What is the Triangle Similarity Theorem?

Back

The Triangle Similarity Theorem states that if two triangles have corresponding angles that are equal, then the triangles are similar, meaning their corresponding sides are in proportion.

Front

What are the conditions for triangle similarity?

Back

The conditions for triangle similarity include: 1) Angle-Angle (AA) Criterion: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. 2) Side-Angle-Side (SAS) Criterion: If one angle of a triangle is equal to one angle of another triangle and the sides including those angles are in proportion, the triangles are similar. 3) Side-Side-Side (SSS) Criterion: If the corresponding sides of two triangles are in proportion, the triangles are similar.

Front

Complete the similarity statement: △ADB ~ _______

Back

△AEC

Front

Complete the similarity statement: △WYX ~ _______

Back

△YWZ

Front

Complete the similarity statement: △ACB ~ _______

Back

△HFG

Front

Complete the similarity statement: △CED ~ _______

Back

△TVU

Front

Complete the similarity statement: △ACB ~ _______ ~ _______

Back

△DCA, △DAB

Front

What does it mean for triangles to be similar?

Back

Triangles are similar if they have the same shape but not necessarily the same size. This means their corresponding angles are equal and their corresponding sides are in proportion.

Front

How can you prove that two triangles are similar?

Back

To prove that two triangles are similar, you can use one of the similarity criteria: AA, SAS, or SSS. You need to show that the conditions of one of these criteria are met.

Front

What is the Angle-Angle (AA) Criterion?

Back

The Angle-Angle (AA) Criterion states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.