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Squaring a Foundation – Which Test Works?

publish date: 2026/05/15 20:40:52.270856 UTC

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A carpenter is building a shed with a 9-ft by 12-ft rectangular foundation. The four sides are already in place but the carpenter needs to verify that all four corners are right angles.

Which single measurement guarantees the foundation has four right-angle corners?

Measuring all four sides to confirm they are equal.

Measuring one interior angle to confirm it is 90°.

Measuring both diagonals to confirm they are equal in length.

Measuring the perimeter to confirm it equals 42 ft.

Correct Answer

Measuring both diagonals to confirm they are equal in length.

Explanation

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. The carpenter uses a tape measure to compare the two diagonals \(AC\) and \(BD\). If \( \overline{AC} = \overline{BD} \), the foundation is a rectangle and all four corners are right angles. This is commonly called squaring a foundation.

Note: checking only one angle also works (if a parallelogram has one right angle, it is a rectangle), but measuring the equal diagonals is the practical technique used by carpenters and picture framers.

Reference

Mathematics for college students

Quizzes you can take where this question appears

Use properties of rectangles to find unknown angle measures and side lengths