The Pythagorean Theorem 1 The Pythagorean Theorem Given

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The Pythagorean Theorem 1

The Pythagorean Theorem 1

The Pythagorean Theorem Given any right triangle, A 2 + B 2 = C

The Pythagorean Theorem Given any right triangle, A 2 + B 2 = C 2 C A B 2

Example In the following figure if A = 3 and B = 4, Find

Example In the following figure if A = 3 and B = 4, Find C. A 2 + B 2 = C 2 32 + 42 = C 2 9 + 16 = C 2 C A 5 = C B 3

Practice 1) A = 8, B = 15, Find C C = 17 2)

Practice 1) A = 8, B = 15, Find C C = 17 2) A = 7, B = 24, Find C C = 25 3) A = 9, B= 40, Find C C = 41 A C 4) A = 10, B = 24, Find C C = 26 5) A = 6, B = 8, Find C 6) A = 9, B = 12, Find C C = 10 B C = 15 4

Example In the following figure if B = 5 and C = 13, Find

Example In the following figure if B = 5 and C = 13, Find A. A 2 + B 2 = C 2 A 2 +52 = 132 C A B A 2 + 25 = 169 A 2 = 144 A = 12 5

Practice 1) A=8, C =10 , Find B B=6 2) A=15, C=17 , Find

Practice 1) A=8, C =10 , Find B B=6 2) A=15, C=17 , Find B B=8 3) B =10, C=26 , Find A A = 24 4) A =12, C=16, Find B B = 10. 6 5) B =5, C=10, Find A 6) A=11, C=21, Find B A = 8. 7 B = 17. 9 C A B 6

“Real-World” The top of a ladder rests against a wall, 23 feet above the

“Real-World” The top of a ladder rests against a wall, 23 feet above the ground. The base of the ladder is 6 feet away from the wall. What is the length of the ladder? Step 1: Draw a sketch and label the parts. Step 2: Determine whether you are looking for the leg or hypotenuse of the right triangle. Step 3: Solve the missing length. 7

AREA Find the area of each figure 1. 2. 8

AREA Find the area of each figure 1. 2. 8

Given the lengths of three sides, how do you know if you have a

Given the lengths of three sides, how do you know if you have a right triangle? Given A = 6, B=8, and C=10, describe the triangle. A 2 + B 2 = C 2 C A 62 +82 = 102 36 + 64 = 100 B 100 = 100 9 This is true, so you have a right triangle.

If C 2 < A 2 + B 2 , then you have an

If C 2 < A 2 + B 2 , then you have an acute triangle. Given A = 4, B = 5, and C =6, describe the triangle. C 2 = A 2 + B 2 62 = 42 + 52 36 = 16 + 25 36 < 41 A B C 36 < 41, so we have an acute triangle. 10

If C 2 > A 2 + B 2 , then you have an

If C 2 > A 2 + B 2 , then you have an obtuse triangle. Given A = 4, B = 6, and C =8, describe the triangle. C 2 = A 2 + B 2 82 = 42 + 62 A B 64 = 16 + 36 64 > 52 C 64 > 52, so we have an obtuse triangle. 11

Describe the following triangles as acute, right, or obtuse 1) A=10, B=15, C=20 2)

Describe the following triangles as acute, right, or obtuse 1) A=10, B=15, C=20 2) A=2, B=5, C=6 obtuse 3) A=12, B=16, C=20 right C A 4) A=11, B=12, C=14 acute 5) A=2, B=3, C=4 obtuse B 6) A=1, B=7, C=7 acute 12