Problem preview
G-SRT.4 Warmup M2-049-A09-V01

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

Use the Pythagorean Theorem after a similarity proof

Problem

A triangle has been proved right, and its legs are \(9\) and \(12\). Use the Pythagorean Theorem to find the missing hypotenuse length.

Big Picture

What this problem is really about

Once the triangle is known to be right, the key is assigning the two legs and the hypotenuse correctly. We’ll square and add the leg lengths, take the positive square root for the missing side, and check both the Pythagorean equation and the fact that the hypotenuse must be longest.

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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 Pythagorean Theorem after a similarity proof