Geometry Quiz - Section 8.2 Converse of the Pythagorean Theorem

If the square of the longest side of a triangle equals the sum of the squares of the other two sides, then the triangle is a right triangle.

• True

• False

A triangle with side lengths 3, 4, and 5 satisfies the converse of the Pythagorean Theorem.

• True, using the pythagorean theorem 36 = 36 proving the converse of the pythagorean theorem

• False, 25 does not equal 36 thus disproving the converse of the pythagorean theorem

• True, using the pythagorean theorem 25 = 25 proving the converse of the pythagorean theorem

• True, the side lengths of a triangle are greater than the hypotenuse of the triangle forming a right triangle.

• False, the following equation above states the equation for an obtuse triangle.

• False, the following equation above states the equation for an acute triangle.

• I don't know I want to cry

The converse of the Pythagorean Theorem can be used to prove that a given triangle is acute.

• True, it is used to prove all triangles and their angles

• False, it is used to prove only right triangles.

For a triangle with sides 6, 8, 10, the converse of the pythagorean theorem confirms that it is a right triangle?

• True

• False

For each of the following sets of side lengths, determine whether the triangle is a right triangle using the converse of the Pythagorean Theorem. Show your work.

a = 7

b = 24

c = 25

• Yes, 625 = 625

• Yes, 725 = 725

For each of the following sets of side lengths, determine whether the triangle is a right triangle using the converse of the Pythagorean Theorem. Show your work.

a = 8, b = 15, c = 17

• Yes, 289 = 289

• Right triangle: 225 = 225

• obtuse triangle: 225 < 289

• acute triangle: 225 > 189

• Right triangle: 676 = 676

• obtuse triangle: 676 < 900

• acute triangle: 900 < 676

A builder is verifying whether a triangular roof frame is square by measuring its sides as 6 feet, 8 feet, and 10 feet. Use the converse of the Pythagorean Theorem to determine whether the roof frame is a right triangle.

• Yes, 100 = 100 square units creating a right triangle

• No, 110 does not equal 100 thus creating an acute triangle

• No, 90 does not equal 100 thus creating an obtuse triangle