Back to Establish AA similarity criterion — Problem 4 · 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

$Two right triangles. Left triangle ABC has a right angle at C and 28° at A. Right triangle DEF has a right angle at F and 28° at D. The right triangle is smaller.$

Right triangle $\triangle ABC$ has $\angle C = 90\degree$ and $\angle A = 28\degree$ . Right triangle $\triangle DEF$ has $\angle F = 90\degree$ and $\angle D = 28\degree$ . Are the triangles similar?

Yes — $\triangle ABC \sim \triangle DEF$ by AA, because $\angle C = \angle F = 90\degree$ and $\angle A = \angle D = 28\degree$ .

No — right triangles are only similar if their hypotenuses are proportional.

Yes — all right triangles are similar to each other.

Cannot determine — we need to know the side lengths.