AnswersFoundations of Math 1Converse to the Pythagorean Theorem — QuizQuestion 1
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Converse to the Pythagorean Theorem — Quiz

Question 1 • Foundations of Math 1

The areas of the squares formed by the side lengths of the triangles are given for each given triangle. Which triangles are right triangles? Choose three correct answers. (Figures are not drawn to scale.)

Answer
A
Image with description A right triangle is surrounded by three squares. The square that shares a side with the shorter leg is labeled 7 inches squared. The square that shares a side with the longer leg is labeled 24 inches squared. The square that shares a side with the hypotenuse is labeled 25 inches squared.
B
Image with description A right triangle is surrounded by three squares. The square that shares a side with the shorter leg is labeled 64 inches squared. The square that shares a side with the longer leg is labeled 225 inches squared. The square that shares a side with the hypotenuse is labeled 289 inches squared.
C
Image with description A right triangle is surrounded by three squares. The square that shares a side with the shorter leg is labeled 25 inches squared. The square that shares a side with the longer leg is labeled 144 inches squared. The square that shares a side with the hypotenuse is labeled 169 inches squared.
D
Image with description A right triangle is surrounded by three squares. The square that shares a side with the shorter leg is labeled 9 inches squared. The square that shares a side with the longer leg is labeled 16 inches squared. The square that shares a side with the hypotenuse is labeled 25 inches squared.
E
Image with description A right triangle is surrounded by three squares. The square that shares a side with the shorter leg is labeled 10 inches squared. The square that shares a side with the longer leg is labeled 24 inches squared. The square that shares a side with the hypotenuse is labeled 26 inches squared.
F
Image with description A right triangle is surrounded by three squares. The square that shares a side with the shorter leg is labeled 6 inches squared. The square that shares a side with the longer leg is labeled 8 inches squared. The square that shares a side with the hypotenuse is labeled 10 inches squared.

Explanation

A triangle is right if the areas of the squares on its two legs add up to the area of the square on its hypotenuse. For B, 64 + 225 = 289; for C, 25 + 144 = 169; and for D, 9 + 16 = 25. The other choices do not satisfy this relationship.

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