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G-SRT.4 Core M2-049-R01-V02

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

Use parallel segments to derive proportional sides

Problem

In triangle \(PQR\), \(ST~\parallel~QR\) with \(PS~=~3\), \(SQ~=~9\), and \(PT~=~4\). Establish \(\triangle~PST~∼~\triangle~PQR\) by \(AA\), solve \(PS/SQ~=~PT/TR\) for TR, then verify the equal whole-side ratios \(PS/PQ\) and \(PT/PR\).

Unworked triangle PQR with S on PQ, T on PR, ST marked parallel to QR, PS=3, SQ=9, PT=4, and TR unknown; no missing length, ratio check, or scale factor is shown. Open full size
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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 parallel segments to derive proportional sides