THE PYTHAGOREAN THEOREM

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The Pythagorean Theorem

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Presentation transcript:

THE PYTHAGOREAN THEOREM An Introduction to Triangles

THE PYTHAGOREAN THEOREM Given any Right Triangle, A2 + B2 = C2 C A B

How do you use the Pythagorean Theorem Let A = 3 and B = 4 C2 = A2 + B2 C2 = 32 + 4 2 C2 = 9 + 16 C = 5 C A B

You can prove the Pythagorean Theorem with the following: Given a piece of graph paper, make a right triangle. Then make squares of the right triangle. Then find the square’s areas.

Solve the problems below using the Pythagorean Theorem 1) A=8, B= 15, Find C 2) A=7, B= 24, Find C 3) A=9, B= 40, Find C 4) A=10, B=24, Find C 5) A =6, B=8, Find C 6) A =7, B=10, Find C 7) A =4, B =5, Find C 8) A=18, B=80, Find C C A B

How do you solve for A or B? Let B = 5 and C = 13 A2 + B2 = C2 A2 +52 = 132 A2 + 25 = 169 A2+25-25=169-25 A2 = 144 A = 12 C A B

Solve the problems below using the Pythagorean Theorem 1) A=8, C =10 , Find B 2) A=15, C=17 , Find B 3) B =10, C=26 , Find A 4) A=15, B=20, Find C 5) A =12, C=16, Find B 6) B =5, C=10, Find A 7) A =6, B =8, Find C 8) A=11, C=21, Find B C A B

Given the lengths of three sides, how do you know if you have a right triangle? Let A = 6, B=8, and C=10 A2 + B2 = C2 62 +82 = 102 36 + 64 = 100 This is true, so you have a right triangle. C A B

If A2 + B2 > C2, you have an acute triangle. Given A = 4, B = 5, and C =6, describe the triangle. A2 + B2 = C2 42 + 52 = 62 16 + 25 = 36 41 > 36, so we have an acute triangle. A B C

If A2 + B2 < C2, you have an obtuse triangle. Given A = 4, B = 6, and C =8, describe the triangle. A2 + B2 = C2 42 + 62 = 82 16 + 36 = 64 52 < 64, so we have an obtuse triangle. A B C

Describe the following triangles as acute, right, or obtuse 1) A=9, B=40, C=41 2) A=10, B=15, C=20 3) A=2, B=5, C=6 4) A=12, B=16, C=20 5) A=11, B=12, C=20 6) A=2, B=3, C=4 7) A=1, B=7, C=7 8) A=90, B=120, C=150 C A B