Back to Establish AA similarity criterion — Problem 3 · 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

$Two parallel lines cut by two transversals meeting at point E between the lines. Triangle ABE on the left and triangle DCE on the right share vertex E. Matching angle marks show angle A equals angle D and angle B equals angle C.$

In the figure, lines $\ell$ and $m$ are parallel, and two transversals intersect them, forming $\triangle ABE$ and $\triangle DCE$ as shown. Which pair of triangles is similar by AA, and what is the correct correspondence?

$\triangle ABE \sim \triangle DCE$ with correspondence $A \leftrightarrow D$ , $B \leftrightarrow C$ , $E \leftrightarrow E$ .

$\triangle ABE \sim \triangle CDE$ with correspondence $A \leftrightarrow C$ , $B \leftrightarrow D$ , $E \leftrightarrow E$ .

The triangles are not similar because no angle measures are given.

$\triangle ABE \sim \triangle DCE$ with correspondence $A \leftrightarrow C$ , $B \leftrightarrow D$ , $E \leftrightarrow E$ .