Back to Establish AA similarity criterion — Problem 1 · 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

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Fluency Practice

$Two triangles. Left triangle ABC has a 40° angle at A and 75° angle at B. Right triangle DEF has a 40° angle at D and 75° angle at E. The right triangle is larger than the left.$

In the diagram, $\triangle ABC$ has $\angle A = 40\degree$ and $\angle B = 75\degree$ . Triangle $\triangle DEF$ has $\angle D = 40\degree$ and $\angle E = 75\degree$ . Which conclusion is correct?

$\triangle ABC \cong \triangle DEF$ because two pairs of angles are equal.

$\triangle ABC \sim \triangle DEF$ by AA, because $\angle A = \angle D$ and $\angle B = \angle E$ .

The triangles cannot be similar because the third angle $\angle C$ is not given.

More information about the side lengths is needed to determine similarity.