Converse to the Pythagorean Theorem

Question 1

Which best explains why this triangle is or is not a right triangle?

Revolt · Accepted Answer

D: This triangle is a right triangle: .

Question 2

Which of these four sets of side lengths will form a right triangle?Set 110 cm, 26 cm, 24 cmSet 24 in., 2 in., 6 in.Set 314 mm, 13 mm, 15 mmSet 410 ft, 30 ft, 20 ft

Revolt · Accepted Answer

A: Set 1

Question 3

Jackie plans to place a rectangular piece of art inside a rectangular frame. She considers a piece of art that is 0.5 meters long, 1.2 meters wide, and has a diagonal length of 1.3 meters.Which is true regarding the art piece?

Revolt · Accepted Answer

A: The art is rectangular because .

Question 4

Chelsea is making a kite in the shape of a triangle. To determine if the triangle is a right triangle, Chelsea completed the following steps.Step 1:Find the side lengths of the triangle: 30 inches, 24 inches, 18 inches. Step 2: Substitute the values into the Pythagorean theorem: .Step 3:Combine like terms: .Step 4: Evaluate each side: .Chelsea says the triangle is not a right triangle. Which best describes the accuracy of her explanation?

Question 5

A builder set up a wooden frame in which to pour concrete for a foundation to a house. The length of the wooden frame is 24 feet. The width is 32 feet. The diagonal is 40 feet. Which best describes the foundation?

Revolt · Accepted Answer

D: The foundation may be a rectangle: .

Question 6

In an isosceles triangle, the longest side measures c units. The other sides of the triangle measure a units. Which equation can be used to determine if the triangle is a right triangle?

Question 7

The areas of the squares created by the side lengths of the triangle are shown. Which best explains whether this triangle is a right triangle?[Not drawn to scale]

Revolt · Accepted Answer

B: Based on the converse of the Pythagorean theorem, the triangle is not a right triangle because .

Question 8

Jeremy is trying to explain why a triangle with side lengths 35, 30, 60 is not a right triangle. His explanation is shown below.Step 1: Step 2: Step 3: Step 4: Which best describes Jeremy’s explanation?

Revolt · Accepted Answer

C: Jeremy’s explanation is inaccurate. He incorrectly combined terms in step 2.

Question 9

Which of these four sets of side lengths will form a right triangle?Set 16 cm, 7 cm, cmSet 28 in., in., in.Set 3 mm, 4 mm, mmSet 49 ft, ft, 6 ft

Revolt · Accepted Answer

B: Set 2

Question 10

Which best explains why this triangle is or is not a right triangle?

Converse to the Pythagorean Theorem Answers

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