Pythagorean Theorem Review

The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2). At which points could the vertex of the right angle in the triangle be located? Check all that apply.

• (–1, 1)

• (4, -2)

• (1,1)

• (2, -2)

• (4, -1)

Which inequalities are true? Select the three correct answers.

• 0 < √8

• √8 < 2

• √8 > √7

• √8 < 3

• √8 > 8

What is the length of the unknown leg in the right triangle?

• 8 cm

• 16 cm

• 20 cm

• 40 cm

Holly and Tamar completed the work in the table to determine if a triangle with side lengths of 40, 42, and 58 is a right triangle. Which best describes the accuracy of their solutions?

• Holly is correct.

• Tamar is correct.

• Neither Holly nor Tamar are correct.

• Both Holly and Tamar are correct.

Nadine is making a quilt. She can use a rectangle of any length and width, as long as the angles in the shape are right angles. Nadine can use Fabric 1. Which other pieces of fabric can Nadine use in the quilt? Check all that apply.

• Fabric 2

• Fabric 3

• Fabric 4

• Fabric 5

• Fabric 6

Which is a right triangle formed using a diagonal through the interior of the cube?

• Triangle BDH

• Triangle DCB

• Triangle GDC

• Triangle GHE

Which statements are true about the unknown side length in this right triangle? Check all that apply.

• The equation a² + (√13)² = 6² can be used to find the unknown leg length.

• The equation (√13)² + b² = 6² can be used to find the unknown leg length.

• The equation (√13)² + 6² = c² can be used to find the unknown leg length.

• The length of the unknown leg is √23 meters.

• The length of the unknown leg is 7 meters

A diagonal of a cube measures √750 cm. The diagonal of a face measures √500 cm.

In centimeters, what is the length of an edge of the cube? Round the answer to the nearest tenth.

Which expression will equal a rational product even though it is multiplying an irrational number times another irrational number?

• $\left(\sqrt{11}\right)\left(\sqrt{11}\right)$

• $\left(4.7813265...\right)\left(\sqrt{5}\right)$

• $\left(\pi\right)\left(3.785492...\right)$

• $\left(\sqrt{21}\right)\left(\pi\right)$

Tamika builds a wooden skateboard ramp. The ramp measures 63 centimeters, and the length of its horizontal base is 60 centimeters, as shown. In centimeters, what is the approximate height of the ramp? Round the answer to the nearest tenth of a centimeter.