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G-SRT.4 Warmup M2-049-A02-V01

Prove triangle-similarity theorems, including proportional segments and the Pythagorean Theorem via similarity.

Use the side-splitter theorem to find a missing segment

Problem

Use the side-splitter theorem to find the missing segment: \(DE\) parallel \(BC\), \(AD=4\), \(DB=6\), \(AE=x\), \(EC=9\)

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

The side-splitter theorem relates the two pieces on one triangle side to the corresponding two pieces on the other. We’ll verify the interior segment is parallel to the third side, keep upper-over-lower order on both sides, solve the resulting proportion, and compare the simplified ratios to check the missing length.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-SRT.4
Category
Geometry
Domain
Similarity, Right Triangles, and Trigonometry
Objective
Prove triangle-similarity theorems, including proportional segments and the Pythagorean Theorem via similarity.
Problem type
Use the side-splitter theorem to find a missing segment