AnswersFoundations of Math 1Converse to the Pythagorean Theorem

Converse to the Pythagorean Theorem — Quiz Answers

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1
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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.)

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.
2
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Tasha assembled a picture frame that is advertised as rectangular. The completed frame is 14 inches long and 10 inches wide. She measured the diagonal length across the frame as 20 inches. Which best explains why the frame cannot actually be rectangular?

A
open paren 14 plus 10 close paren squared is not equal to 20 squared
B
14 plus 10 is not equal to 20
C
14 squared plus 10 squared is not equal to 20 squared
D
open paren 14 squared plus 10 squared close paren squared is not equal to 20 squared
3

Jude is making a door for a door frame with an opening that measures 9 feet by 3 feet. Which diagonal length should he use to make a door that fits in the door frame?

A
square root of 90 feet
B
12 feet
C
square root of 72 feet
D
10 feet
4

A teacher asks her students to design a game board for a class project. The dimensions of the boards created by four students are shown here. Angela length: 20 cm width: 21 cm diagonal: 29 cm Bradley length: 9 in. width: 9 in. diagonal: 9 in. Carlton length: 25 cm width: 30 cm diagonal: 35 cm Della length: 10 in. width: 12 in. diagonal: 15 in. Whose game board could be a rectangle?

A
Angela
B
Carlton
C
Della
D
Bradley
5

Jackie plans to place a rectangular piece of art inside a rectangular frame. She considers a piece of art that is 0 point 5 meters long, 1 point 2 meters wide, and has a diagonal length of 1 point 3 meters. Which is true regarding the art piece?

A
The art is not rectangular because 0 point 5 squared plus 1 point 2 squared is not equal to 1 point 3 squared .
B
The art is rectangular because 1 point 2 squared minus 0 point 5 squared is less than 1 point 3 squared .
C
The art is rectangular because 0 point 5 squared plus 1 point 2 squared is equal to 1 point 3 squared .
D
The art is not rectangular because 0 point 5 squared plus 1 point 2 squared is greater than 1 point 3 squared .
6

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?

A
The foundation may be a rectangle: 24 squared plus 32 squared is equal to 40 squared .
B
The foundation cannot be a rectangle: square root of 24 squared plus 32 squared end root is not equal to 40 squared .
C
The foundation cannot be a rectangle: 24 plus 32 is not equal to 40 .
D
The foundation cannot be a rectangle: open paren 24 plus 32 close paren squared is not equal to 40 squared .
7

Which of these four sets of side lengths will form a right triangle? Set 1 4 cm, 5 cm, 6 cm Set 2 8 in., 12 in., 20 in. Set 3 10 mm, 20 mm, 30 mm Set 4 12 ft, 16 ft, 20 ft

A
Set 1
B
Set 2
C
Set 3
D
Set 4
8

Which of these four sets of side lengths will form a right triangle? Set 1 6 cm, 7 cm, square root of 12 cm Set 2 8 in., square root of 29 in., square root of 35 in. Set 3 square root of 3 mm, 4 mm, square root of 5 mm Set 4 9 ft, square root of 26 ft, 6 ft

A
Set 1
B
Set 2
C
Set 3
D
Set 4
9

Which triangle side lengths form a right triangle? Choose two correct answers.

A
5, 6, 7
B
6, 8, 14
C
10, 12, 15
D
8, 15, 17
E
15, 20, 25
F
16, 18, 20
10

Which of these four sets of side lengths will form a right triangle? Set 1 10 cm, 26 cm, 24 cm Set 2 4 in., 2 in., 6 in. Set 3 14 mm, 13 mm, 15 mm Set 4 10 ft, 30 ft, 20 ft

A
Set 1
B
Set 2
C
Set 3
D
Set 4

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