Pythagorean and Its Converse

A builder is verifying whether a triangular roof frame is square by measuring its sides as 6 feet, 8 feet, and 10 feet. Use the converse of the Pythagorean Theorem to determine whether the roof frame is a right triangle.

• Yes, 100 = 100 square units creating a right triangle

• No, 110 does not equal 100 thus creating an acute triangle

• No, 90 does not equal 100 thus creating an obtuse triangle

A landscaper wants to ensure a triangular garden has a right angle by measuring sides 9, 12, and 15 meters. Verify whether the garden forms a right triangle.

• No, 225 does not equal 348 thus creating an obtuse triangle

• No, 225 does not equal 189 thus creating an acute triangle

• Yes, 225 = 225 thus the garden forms a right triangle

The two smaller sides of a triangle are 2 3/4 and 5 1/2. What is a possible length of the third side to make the triangle right? Show your work.

• c = 5.41

• c = 6.15

• c = 5.24

• c = 6.81

Larry attached a string from the top of the flagpole to the ground.  The flagpole is 26 feet high and the string is 18 feet away from the flagpole.  How long is the string? 

• 352 feet 

• 31.6 feet 

• 44 feet 

• 6.6 feet 

If three sides of a right triangle are 50, 40, and 30, which side is the hypotenuse?

• 50

• 40

• 30

If three sides of a right triangle are 5, 3, and 4, which side is the hypotenuse?

• 5

• 3

• 4

Do the side lengths 9, 12, and 17 make a right triangle?

• Yes

• No

Which set of side lengths does not form a right triangle?

• 38, 80, 90

• 16, 63, 65

• 36, 77, 85

• 14, 15, 29

Which set of side lengths form a right triangle?

• 3, 4, 7

• 33, 56, 65

• 66, 72, 97

• 10, 15, 25

The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide?

• 8 feet

• 5.29 feet

• 10 feet

• 14 feet