Unit 8 Pythagorean Theorem

Ranee is creating a diagram to prove that a certain triangle is a right triangle. In her diagram she uses three white quadrilaterals that are squares. Which diagram could be the one that Ranee is creating?

• A

• B

• C

• D

Caleb has a piece of rectangular paper that is 12 inches wide by 16 inches long. He drew a straight line along the diagonal of the paper. What is the length of the line Caleb drew?

• C. 20 inches

• D. 28 inches

A triangle with side lengths a, b, and c is shown below. Which statement about the side lengths must be true?

• A. a + b > c

• B. b + c < a

• C. a + b < c

• D. a + c < b

Using the Pythagorean Theorem, what is the value of c?

• C. 6 units

• D. 20 units.

Olivia is shipping a baton and a few other things to a friend as a gift. The box measures 8 inches, by 9 inches, by 1 foot. She places the baton in the box as shown below. What is the length, in inches, of the baton that she placed in the box?

• 15 inches

• 17 inches

• 19 inches

• 20 inches

This question is worth 2 credits. Triangle RST has side lengths of 8 centimeters, 10 centimeters, and 13 centimeters. Using the Pythagorean theorem (which states that for a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side), determine if triangle RST is a right triangle.

• Triangle RST is a right triangle because 8² + 10² equals 13².

• Triangle RST is not a right triangle because 8² + 10² does not equal 13².

• Triangle RST could be a right triangle if computed differently.

Triangle DEF is a right triangle with a right angle at vertex F. Side DF has a length of 9 inches and side FE has a length of 12 inches. What is the length, in inches, of side DE?

• 15 inches

• 18 inches

• 16 inches

• 21 inches