MA.8.GR.1.1 · Geometric Reasoning

The Pythagorean Theorem and Missing Side Lengths: Sample FAST Questions

The Pythagorean Theorem, a^2 + b^2 = c^2, is the headline 8th grade geometry skill for right triangles. Students find a missing hypotenuse, find a missing leg, and apply the theorem to real situations like ladders, ramps, and diagonal distances.

How the FAST tests this benchmark

FAST items include equation editor answers for a side length, multiple choice word problems, and items built on a labeled triangle diagram. Students are expected to know the theorem from memory, and radicands stay whole numbers up to 225, so every side comes out to 15 or less.

Skills students need

Find the hypotenuse of a right triangle
Find a missing leg of a right triangle
Apply the Pythagorean Theorem to real-world problems
Recognize common Pythagorean triples

Try 6 real MA.8.GR.1.1 questions

These come straight from Algebro's 8th grade pre-algebra question bank, easiest first. Answer one, check it, then move to the next.

Question 1 of 6

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Question 1EasyMultiple Choice

A rectangular garden has a diagonal of 26 meters and a length of 24 meters, as shown. What is the width, in meters, of the garden?

Figure may not be drawn to scale

Showcase extra: the real practice and quiz players do not have this button.

Question 5HardMatching

Each row gives the two legs of a right-triangular field. Match each field to its perimeter, in ft.

Pick one match in each row, then check.

	A.36 ft	B.24 ft	C.30 ft
$\text{legs } 6 \text{ and } 8$
$\text{legs } 5 \text{ and } 12$
$\text{legs } 9 \text{ and } 12$

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More 8th grade geometric reasoning benchmarks

MA.8.GR.1.2

Distance Between Two Points on the Coordinate Plane

MA.8.GR.1.3

Triangle Inequality and the Converse of the Pythagorean Theorem

MA.8.GR.1.4

Complementary, Supplementary, Vertical, and Adjacent Angles