Unit 6 Study Guide: Pythagorean Theorem and Volume

Julianne began her proof of the Pythagorean Theorem by dividing a right trapezoid into three triangles. If the bases of the right trapezoid measure 6 in. and 8 in., which of these is an area of one of the three triangles? Select all that apply.

• 24 in²

• 30 in²

• 50 in²

Based on the Pythagorean Theorem, which statement is correct?

• The empty square has a side length of 8 and an area of 64 square units.

• The empty square has a side length of 9.6 and an area of 92 square units.

• The empty square has a side length of 10 and an area of 100 square units.

• The empty square has a side length of 14 and an area of 196 square units.

Yaira wants to use the figure below to explain the converse of the Pythagorean theorem. In order for this figure to be useful, what must be true about the figure?

• area of square a + area of square b = area of square c

• (area of square a)(area of square b) = area of square c

• (area of square b)^2 = area of square c

• area of square a = 2(area of square b)

Which of the following correctly describes the Pythagorean theorem?

• The sum of the lengths of the legs of a right triangle is equal to the length of the hypotenuse.

• The sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

• The product of the lengths of the legs of a right triangle is equal to the length of the hypotenuse.

• The product of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

Three boats in the ocean are located near a buoy as represented by the diagram below. The distance between boats 2 and 3 is known to be 65 miles. Which statements are true? Choose the TWO correct answers.

• The distance between boat 3 and the buoy is 40 miles.

• The distance between boats 1 and 2 is about 16.5 miles.

• The distance between boats 1 and 3 is 50 miles.

• The distance between the buoy and boat 1 is not needed to find the distance between boats 1 and 2.

• The distance between boats 2 and 3 is not needed to find the distance between the buoy and boat 3.

Given: ΔABC is a right triangle with three shaded squares with sides a, b, and c, respectively, where a, b, and c are also the lengths of the sides of the right triangle, such that the area of the square with side a is a² and the area of the square with side b is b² and the area of the square with side c is c². Prove: a² + b² = c² (Pythagorean Theorem). Proving which of the following will prove the Pythagorean Theorem?

• When you subtract the area of the smallest square from the medium square the difference equals the area of the largest square.

• The sides of a right triangle are also the sides of squares.

• ∠A + ∠B = ∠C

• The area of the two smaller squares will add up to the area of the largest square.

Selena is flying a kite, as shown below. The angle formed by the dotted lines is a right angle. How long, in feet, is the kite string?

A 13-meter-long ladder leans against a building with the base of the ladder 5 meters away from the bottom of the building. How many meters above the ground does the ladder meet the building?

A right triangle has a leg measuring 24 units. Which of these statements are correct? Select three that apply.

• If the length of the hypotenuse is 25 units, the length of the other leg is 7 units.

• If the length of the hypotenuse is 26 units, the length of the other leg is 10 units.

• If the length of the hypotenuse is 28 units, the length of the other leg is 14 units.

• If the length of the hypotenuse is 30 units, the length of the other leg is 18 units.

A right pyramid is shown below. The height of the pyramid is 14 units. The distance from the center of the base of the pyramid to the middle of PR at M is 6 units. What is the length of the slant height QM in units? Round your answer to the nearest tenth.