Problem preview
G-SRT.2 Warmup M2-047-A06-V01

Use similarity transformations to decide similarity and explain angle equality and side proportionality in triangles.

Find a missing side length from corresponding sides in similar triangles

Problem

In similar triangles, \(AB\) corresponds to \(DE\) and \(AC\) corresponds to a side of length \(x\). If \(AB=3\), \(DE=6\), and \(AC=4\), find \(x\).

Big Picture

What this problem is really about

A missing side inherits the same factor as a fully known corresponding pair. We’ll establish the actual side matches from the vertex correspondence, compute the target-to-source factor from the known pair, apply it in the same direction to the side paired with the unknown, and verify both ratios agree.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-SRT.2
Category
Geometry
Domain
Similarity, Right Triangles, and Trigonometry
Objective
Use similarity transformations to decide similarity and explain angle equality and side proportionality in triangles.
Problem type
Find a missing side length from corresponding sides in similar triangles