The Pythagorean Theorem and Its Converse

Which side is the hypotenuse?

Which side is the hypotenuse?

• x

• y

• z

Given the following measures of the sides of triangles, which is a right triangle?

• 3 ft, 4 ft, 7 ft

• 33 cm, 56 cm, 65 cm

• 66 yd, 72 yd, 97 yd

• 10 m, 15 m, 25 m

Which set of side lengths does not form a right triangle?

• 48, 55, 73

• 16, 63, 65

• 36, 77, 85

• 14, 15, 29

True or False: When determining whether or not 3 side lengths form a right triangle, add the side lengths of the shortest sides to see if the sum is equal to the length of the longest side.

• True

• False

True or False: To determine if 3 side lengths form a right triangle, add the squares of the two shortest sides to determine if the sum equals the square of the longest side.

• True

• False

Isabella has sticks that are 10cm, 11cm, and 13cm long. Can she place the sticks together to form a right triangle? Justify your answer.

• No, because 10+11 does not equal 13

• No, because 100+121 does not equal 169

• Yes, because 10+11 is greater than 13

• We don't have enough information to determine whether it's a right triangle.

CHALLENGE QUESTION: Alan made a small four-sided table for his office. The opposite sides of the table are 27 inches long and 36 inches long. If the diagonal of the table measures 40 inches, does the table have right angles at the corners? Why or why not?

• Yes, because it's a rectangle and rectangles have 90 degree angles in the corners

• Yes, because 27 + 36 is greater than 40

• No, because 27² + 36² does not equal 40²

• No, because 27 + 36 does not equal 40

Which set of sides would make a right triangle?

• 4,5,6
• 8,10,12
• 5,12,13
• 5,10,12

Find the value of x.

• 7
• 8
• 9
• 10