Back to Establish AA similarity criterion — Problem 5 · 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 $\triangle ABC$ has $\angle A = 50\degree$ , $\angle B = 70\degree$ , and $AB = 6$ cm. Triangle $\triangle DEF$ has $\angle D = 50\degree$ , $\angle E = 70\degree$ , and $DE = 9$ cm. Which statement is true?

$\triangle ABC \sim \triangle DEF$ by AA, and the triangles are also congruent because they share two equal angles.

$\triangle ABC \sim \triangle DEF$ by AA, with scale factor $k = \frac{3}{2}$ from $\triangle ABC$ to $\triangle DEF$ .

The triangles are congruent by ASA because two angles and the included side are given.

The triangles are not similar because their sides are different lengths.