7.1 – Apply the Pythagorean Theorem

In your group, do the following: 1. Find the area of one of the four right triangles baba abab b a c

In your group, do the following: 2. Find the TOTAL area for all four right triangles baba abab b a c 2 2ab

In your group, do the following: 3. Find the area of the tilted square baba abab b a c A = s 2 A = c 2

In your group, do the following: 4. Find the area of the large square baba abab b a c A = s 2 A = (a+b) 2 A = (a+b)(a + b) A = a 2 + 2ab + b 2

In your group, do the following: 5. Write an equation to show the area of the tilted square plus the four triangles equal the area of the large square and simplify baba abab b a c c 2 + 2ab = a 2 + 2ab + b 2 c 2 = a 2 + b 2 Sound familiar?

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