Back to Establish AA similarity criterion — Problem 2 · Task Set 16

Exercises: Establish AA Similarity Criterion

Work through each section in order. Show your reasoning where indicated. For problems that ask you to determine similarity, identify the two angle pairs that allow you to apply AA.

Grade 9·20 problems·~30 min·Common Core Math - HS Geometry·standard·hsg-srt-a-3

Work through problems with immediate feedback

Fluency Practice

Triangle $\triangle PQR$ has $\angle P = 32\degree$ and $\angle Q = 58\degree$ . Triangle $\triangle XYZ$ has $\angle X = 32\degree$ and $\angle Z = 90\degree$ . Are these triangles similar by AA?

Yes — $\angle P = \angle X$ and $\angle Q = \angle Z$ , so $\triangle PQR \sim \triangle XYZ$ by AA.

Yes — $\angle P = \angle X$ and $\angle R = \angle Z$ , so $\triangle PQR \sim \triangle XYZ$ by AA.

No — only one pair of angles is equal.

No — we need to check all three angle pairs first.