Problem preview

G-SRT.4 Warmup M2-049-A09-V03

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 a ladder, wall, and ground form a right triangle, use the Pythagorean Theorem to find the ladder length. The wall and ground legs are \(6\) and \(8\).

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Using the Pythagorean Theorem, 6² + 8² = c², so 36 + 64 = 100 and the ladder length is 10.

Using the Pythagorean Theorem, add the two given sides 6 + 8 = 14, so the ladder length is 14.

Using the Pythagorean Theorem, 6² + 8² = c², so 36 + 64 = 100 and the ladder length is 100.

Using the Pythagorean Theorem, treat the ladder as a leg and write c² + 6² = 8², so c² = 28 and the ladder length is 28.

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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