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Objective The student will be able to: use the Pythagorean Theorem

What is a right triangle? hypotenuse leg right angle leg It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse.

The Pythagorean Theorem In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then a2 + b2 = c2. Note: The hypotenuse, c, is always the longest side.

Find the length of the hypotenuse if 1. a = 12 and b = 16. 122 + 162 = c2 144 + 256 = c2 400 = c2 Take the square root of both sides. 20 = c

Find the length of the hypotenuse if 2. a = 5 and b = 7. 52 + 72 = c2 25 + 49 = c2 74 = c2 Take the square root of both sides. 8.60 = c

Find the length of the hypotenuse given a = 6 and b = 12 180 324 13.42 18

The Pythagorean Theorem 7.3 – Square Roots and The Pythagorean Theorem Find the length of the hypotenuse of the given right triangle. The Pythagorean Theorem: hypotenuse 5 feet a c b 12 feet

The Pythagorean Theorem 7.3 – Square Roots and The Pythagorean Theorem Find the length of the hypotenuse of the given right triangle. The Pythagorean Theorem: hypotenuse 4 feet a c b 7 feet Use the Square Root Table

What are Pythagorean Triples? Three integers that make the equation a2 + b2 = c2 true are called Pythagorean Triples. The numbers 3, 4 and 5 are a very famous Pythagorean Triple. a2 + b2 = c2 32 + 42 = 52 9 + 16 = 25