Problem preview

G-SRT.4 Warmup M2-049-A09-V02

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

Use the Pythagorean Theorem after a similarity proof

Problem

After establishing that the triangle is right, use the Pythagorean Theorem to find the missing leg length. The hypotenuse is \(13\) and \(\text{one}~\text{leg}\) is \(5\).

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Using the Pythagorean Theorem, subtract the side lengths 13 - 5 to get 8, so the missing leg is 8.

Using the Pythagorean Theorem, 5² + b² = 13², so 25 + b² = 169, then b² = 144 and the missing leg is 144.

Using the Pythagorean Theorem, subtract 5² from 13 to get b², so 13 - 25 = -12 and the missing leg is 12.

Using the Pythagorean Theorem, 5² + b² = 13², so 25 + b² = 169, then b² = 144 and the missing leg is 12.

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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