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G-SRT.4 Warmup M2-049-A07-V01

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

Use right-triangle similarity to find a missing length

Problem

Use right-triangle similarity to find the missing length: hypotenuse segments \(4\) and \(9\); altitude \(h\)

Neutral right-triangle similarity reference listing hypotenuse segments 4 and 9 and altitude h, without a solved-proportion triangle. Open full size
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What this problem is really about

An altitude to a right triangle’s hypotenuse creates a geometric-mean relationship, not an additive one. We’ll use the similar smaller triangles to place the altitude between the two hypotenuse pieces in a proportion, solve the resulting square equation, keep the positive length, and verify the original proportion.

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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 right-triangle similarity to find a missing length