Pythagorean Theorem Test

Identify the right triangle in the following set of triangles:

• Triangle ABC with sides AB = 8, BC = 15, AC = 17

• Triangle ABC with sides AB = 3, BC = 4, AC = 5

• Triangle ABC with sides AB = 5, BC = 12, AC = 13

• Triangle ABC with sides AB = 7, BC = 24, AC = 25

If a carpenter is building a right triangle with sides measuring 3 and 4 units, what would be the length of the hypotenuse?

• 7

• 6

• 5

• 8

Calculate the distance between two cities A and B, where the distance between A and a point C is 8 units and the distance between B and C is 15 units.

• 10

• 20

• 17

• 25

State the converse of the Pythagorean theorem in the context of a construction project.

• If a right-angled triangle is used in a construction project, then the square of the length of the longest side is equal to the sum of the squares of the other two sides.

• If a right-angled triangle is used in a construction project, then the square of the length of the longest side is not equal to the sum of the squares of the other two sides.

• If a triangle is not a right triangle in a construction project, then the square of the length of the longest side is equal to the sum of the squares of the other two sides.

• If a triangle is not a right triangle in a construction project, then the square of the length of the longest side is not equal to the sum of the squares of the other two sides.

In a construction project, a right triangle has two legs measuring 6 units and 8 units. What is the distance from the right angle to the hypotenuse?

• 4.8 units

• 7.5 units

• 3.6 units

• 5.2 units

A ladder leaning against a wall forms a right triangle with the wall and the ground. If the ladder is 10 meters long and the distance from the base of the ladder to the wall is 6 meters, how far up the wall does the ladder reach?

• 15 meters

• 12 meters

• 5 meters

• 8 meters

Which of the following triangles satisfy the Pythagorean theorem in a construction project?

• Triangle with sides 10, 24, 26 units satisfies the Pythagorean theorem.

• Triangle with sides 8, 15, 17 units satisfies the Pythagorean theorem.

• Triangle with sides 9, 12, 15 units satisfies the Pythagorean theorem.

• Triangle with sides 5, 12, 14 units satisfies the Pythagorean theorem.

If a carpenter is building a right triangle with sides measuring 7 and 24 units, what is the length of the hypotenuse?

• 20

• 30

• 15

• 25

Find the missing side length in a right triangle with sides 5 and 12 units long.

• 8

• 10

• 13

• 15

Explain how you can determine if a triangle is a right triangle using the Pythagorean theorem.

• If a ladder is leaning against a wall and the distance from the base of the ladder to the wall and the length of the ladder form a right triangle, then the triangle is a right triangle.

• If a flagpole is standing upright and the height of the flagpole and the shadow it casts on the ground form a right triangle, then the triangle is a right triangle.

• If a ramp is placed against a truck and the length of the ramp and the height of the truck form a right triangle, then the triangle is a right triangle.

• If a wire is stretched across two poles and the distance between the poles and the length of the wire form a right triangle, then the triangle is a right triangle.