7.1 – Apply the Pythagorean Theorem. Pythagorean Theorem: leg hypotenuse a b c c 2 = a 2 + b 2 (hypotenuse) 2 = (leg) 2 + (leg) 2 If a triangle is a right.

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7.2 Converse of Pythagorean Theorem

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7.1 – Apply the Pythagorean Theorem

Pythagorean Theorem: leg hypotenuse a b c c 2 = a 2 + b 2 (hypotenuse) 2 = (leg) 2 + (leg) 2 If a triangle is a right triangle, then (hypotenuse) 2 = (leg) 2 + (leg) 2

1. Find the value of x. c 2 = a 2 + b 2 x 2 = x 2 = x 2 = 1521 x = 39 H

1. Find the value of x. c 2 = a 2 + b 2 x 2 = x 2 = x 2 = 97 H

1. Find the value of x. c 2 = a 2 + b 2 x 2 = x 2 = x 2 = 45 H

1. Find the value of x. c 2 = a 2 + b = x = x = x 2 H

1. Find the value of x. c 2 = a 2 + b = x = x = x 2 H

1. Find the value of x. c 2 = a 2 + b = x = x = x 2 H

2. Find the area of the isosceles triangle. c 2 = a 2 + b = h = h = h in 2 H H

2. Find the area of the isosceles triangle. c 2 = a 2 + b = h = h = h 2 4 cm 2 H

2. Find the area of the isosceles triangle. c 2 = a 2 + b = h = h = h 2 24 m 2 24 H

7.2 – Converse of the Pythagorean

Pythagorean Theorem Converse: If c 2 = a 2 + b 2, then the triangle is a right triangle a b c

Acute Triangle: If c 2 < a 2 + b 2, then the triangle is acute a b c

Obtuse Triangle: If c 2 > a 2 + b 2, then the triangle is obtuse a b c

For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! c 2 = a 2 + b = = = > > > 8 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE a. 8, 15, 17

3 + 4 > 9 b. 3, 4, 9 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE 7 > 9 For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!

c 2 = a 2 + b = c. Triangle: YES or NO ACUTE, RIGHT, or OBTUSE For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! 10, 11, > > > = <

c 2 = a 2 + b 2 61 = = 61 d. For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! Triangle: YES or NO ACUTE, RIGHT, or OBTUSE > > > 5

c 2 = a 2 + b = e. For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! Triangle: YES or NO ACUTE, RIGHT, or OBTUSE > > > 3.6 >

c 2 = a 2 + b = f. 4.3, 5.2, 6.1 For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! Triangle: YES or NO ACUTE, RIGHT, or OBTUSE > > > 4.3 <

, 5, odd, 24, 26, 31, 39, odd, odd, 25 HW Problem 7.1 #26 Ans: c 2 = a 2 + b = a = a = a 2 a HH 4 = a c 2 = a 2 + b 2 x 2 = x 2 = x 2 = 65