LT 5.7: Apply Pythagorean Theorem and its Converse

Math Humor What do you call a prisoner’s poem? A converse!

Pythagorean Theorem a2+b2=c2 In a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. a2+b2=c2 Hypotenuse Leg Leg

Example Find the hypotenuse. 20 c 12 16

Example Find x: 18.3 20 x 8

When the lengths of the sides on a right triangle are all integers. Pythagorean Triple When the lengths of the sides on a right triangle are all integers. Common Triples 3,4,5 5,12,13 8,15,17 7,24,25

Examples Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. Check with a classmate 1) 7, 12, 16 2) 11, 18, 34 3) 3.8, 4.1, 5.2 4) 30, 40, 50

Example The hypotenuse of a right triangle measures 18 meters. One leg measures 12 meters. Find the length of the other leg and leave it in simplest radical form.

Example Determine if the following lengths can form a triangle. If they form a triangle, classify it according to it’s angle measures. 3, 4, 10 10, 2, 8 42, 56, 70 9, 8, 7