Lesson 8.1 The Pythagorean Theorem

The artist will use small congruent square tiles to cover each region without any gaps or overlaps. Based on the information, which statement is true?

• The number of tiles needed to cover Region X is the same as the number of tiles needed to cover both Region Y and Region Z.

• The number of tiles needed to cover Region Y is the same as the number of tiles needed to cover both Region X and Region Z.

• The number of tiles needed to cover Region Z is the same as the number of tiles needed to cover both Region X and Region Y.

• The number of tiles needed to cover Region Z is greater than the number of tiles needed to cover both Region X and Region Y.

Parallelogram JKLM is shown. Which statement proves that parallelogram JKLM is a rectangle?

The length of a rectangular frame is 15 inches, and the width of the frame is 8 inches. What is the length of a diagonal of this frame in inches?

Mathematical Equivalence

OFF

The dimensions of a rectangular piece of paper are 8.5 inches and 11 inches. Veronica folded the piece of paper along its diagonal. Which measurement is closest to the length of the diagonal in inches?

• 6.24 in.

• 19.5 in.

• 6.98 in.

• 13.9 in.

Based on the diagram, what is the distance in feet from the top of the pole to the bottom of the stake?

Mathematical Equivalence

OFF

Which measurement is closest to the length of the ramp in feet?

• 8.5 ft

• 10.5 ft

• 9.5 ft

• 13.5 ft

Which equation could be used to find the missing side length of the right triangle shown?

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Which of the following statements is NOT a true statement?

• The legs of a triangle are the sides adjacent to the right angle.

• The hypotenuse is directly across from the right angle.

• The Pythaogrean Theorem can only be used with right triangles.

• The hypotenuse is always the shortest side length.

Find the missing side length. Round to the nearest tenth if necessary.

Mathematical Equivalence

OFF

Find the missing side length. Round to the nearest tenth if necessary.

Mathematical Equivalence

OFF