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G-SRT.3 Warmup M2-048-A07-V01

Use similarity transformations to establish the AA similarity criterion.

Use AA-similar triangles to match corresponding angles and find a missing angle or variable

Problem

The triangles are similar by \(AA\). Triangle \(ABC\) is similar to triangle \(DEF\), and \(\angle~B=62^{\circ}\). Find the measure of angle \(E\).

Unworked triangle configuration showing exactly the supplied angle, parallel, or right-angle evidence. Open full size
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What this problem is really about

The ordered similarity statement identifies corresponding angles before any calculation. We’ll expand the first-second-third vertex mapping, locate the requested angle’s partner, use congruence of corresponding angles to transfer the known measure, and verify that the result names the requested vertex with degree units.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-SRT.3
Category
Geometry
Domain
Similarity, Right Triangles, and Trigonometry
Objective
Use similarity transformations to establish the AA similarity criterion.
Problem type
Use AA-similar triangles to match corresponding angles and find a missing angle or variable