Converse to the Pythagorean Theorem

Find the length of the missing side. 

• 17 cm

• 22 cm

• 15 cm

• 13 cm

Find the measure of h.

• 13

• 20

• 9.7

• 10

_{^{Find the missing side}}

• 48

• 108

• 83.6

• 72

Is this triangle a right triangle?

• yes

• no

A triangle has sides of lengths 9, 40, and 41. Using the converse of the Pythagorean theorem, determine if it is a right triangle.

• Yes

• No

Use the converse of the Pythagorean Theorem to determine if the triangle is acute, right, or obtuse.

• Acute

• Right

• Obtuse

Using the converse of the Pythagorean theorem, which set of side lengths shows that a triangle is acute?

• 3, 4, 6

• 5, 12, 13

• 8, 15, 16

• 6, 8, 9

What does the Converse of the Pythagorean Theorem state?

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

• If a triangle has sides of length a, b, and c, and if a²+b²=c², then the angle opposite the side of length c is a right angle

• The ratio of the circumference of a circle to the length of its diameter

• A set of three positive integers a, b, and c such that a²+b²=c²

Using the converse of the Pythagorean theorem, determine if the following triangle is a right triangle: sides are 21 cm, 28 cm, and 35 cm.

• Yes

• No

Which statement is an important part of the proof of the converse of the Pythagorean theorem?

• It must be assumed that the Pythagorean theorem is true.

• It must be assumed that the sum of the lengths of any two sides of a triangle are less than the length of the third side.

• It must be assumed that the Pythagorean theorem is false.

• It must be assumed that the sum of the lengths of any two sides of a triangle are greater than the length of the third side.