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7.2 The Pythagorean Theorem and its Converse. What you’ll learn: To use the Pythagorean Theorem To use the converse of the Pythagorean Theorem. Theorem 7.4. The Pythagorean Theorem
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7.2 The Pythagorean Theorem and its Converse What you’ll learn: To use the Pythagorean Theorem To use the converse of the Pythagorean Theorem
Theorem 7.4 The Pythagorean Theorem In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. a²+b²=c² A leg hypotenuse b c C B a leg
Theorem 7.5 Converse of the Pythagorean Theorem If the sum of the squares of the measures of 2 sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle. If a²+b²=c² then ABC is a right . A c b C B a
Pythagorean Triples Pythagorean Triple – 3 whole numbers that satisfy the equation a²+b²=c². Some common Pythagorean triples are: 3,4,5 7,24,25 8,15,17 9,40,41 More triples can be created by multiplying the numbers by a constant. 3,4,5 6,8,10 15,20,25 30,40,50
7.8 Find x. 9 15.4 6 x x x 1. 2. 3. 17
Determine whether ABC is a right triangle for the given vertices. A(2,7), B(3,6), C(-4,-1)
Determine whether each set of numbers can be the measure of the sides of a right triangle. Then state whether they form a Pythagorean Triple. • 7, 28, 29
