Converse of the Pythagorean Theorem

Do the following squares form a right triangle?  Why or why not?

• No, because 9+15 does not equal 16

• No, because the squares are not equal

• Yes, because the squares are all different sizes

• Yes, becuase 9+15=16

• Yes
• No

Would these side lengths form a right triangle?

• Yes

• No

The lengths of a triangle are given below. Is the triangle obtuse, acute or right?

• Acute

• Right

• Obtuse

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

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.

Use the converse of the Pythagorean Theorem to find the answer choice below whose side lengths do NOT represent a right triangle.

• 6cm, 8cm, 10cm

• 5in, 12in, 13in

• 10m, 20m, 40m

• 8in, 15in, 17in

Would these three sides form a right triangle?

• Yes

• No

Is this triangle a right triangle?

• yes

• no

Find the length of the missing side. 

• 17 cm

• 22 cm

• 15 cm

• 13 cm