7 1 Pythagorean Theorem fguilbert fguilbert fguilbert Objective

7. 1 Pythagorean Theorem fguilbert

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Objective • To use the Pythagorean Theorem to find the lengths of the sides of a Right Triangle. fguilbert

Area of a Square • Area = Length • Width or A = side • side Length = 4 Width = 4 Area= 16 fguilbert

Areas of 3 squares 3 X 3 4 X 4 5 X 5 fguilbert

Arrange them into a triangle 5 X 5 4 X 4 3 X 3 fguilbert

Pythagorean Theorem Add the areas of the 2 smallest squares. Compare to the area of the largest square. fguilbert

Pythagorean Theorem Area = 25 Area =16 9 + 16 =25 Area = 9 fguilbert right triangle

Pythagorean Theorem 6, 7, 8 in length Area = 64 Area =49 36 + 49 = 64 Area = 36 No right fguilbert

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Pythagorean Theorem What did you find? ? fguilbert

Pythagorean Theroem 2 • The sum of the careas of the 2 small squares 2 = equals the b area of the 2 + largest square. a • This is TRUE for all Right triangles. fguilbert

Pythagorean Theorem 2 c 2 b 2 a fguilbert + 2 b = 2 c

Parts of a Right triangle leg hypotenuse longest opposite rt. <. leg fguilbert

Find the Hypotenuse a = 8 b = 15 2 a 2 b 2 c + = 2 2 2 8 + 15 = c 2 64_+ 225 = _c √ 289 = √c 2 17 = c fguilbert 15 17 8

Pythagorean Theorem 2 a 2 b 2 c + = 2 2 2 3 +4 =5 9 + 16 = 25 25 = 25 3 5 golden triangle 4 Multiples of 3, 4, 5 form right fguilbert

Find a if b = 8 & c = 10 2 a + 2 b = 2 2 2 a + 8 = 10 2 a + 64 = 100 2 a = 36 a=6 2 c shortcut 3, 4, 5 6 8, 10 __, multiple of 3, 4, 5 fguilbert

Find a if b = 4 and c= 10 2 a 2 b 2 c + = 2 2 2 a + 4 = 10 2 a + 16 = 100 - 16 2 a = 84 a = 9. 2 fguilbert no shortcut here

The side of a square is √ 8. Find the diagonal. _ _ 2 2 2 (√ 8) +(√ 8 ) = c 4 √ 8 2 c 8 + 8 = _ _ 2 √ 16 =√ c √ 8 4 = c fguilbert

A square has a diagonal 8. Find each side. 8 x x 2 X + = 2 2 X = 64 2 = X 32 X = √ 32 X = 5. 65 fguilbert 2 X 2 8

Find the height (h) of the triangle. 9 2 3 h 6 3 2 h + = 2 9 + h = 81 2 h = 72 h = 8. 5 fguilbert 2 9

In a rectangle, diagonals bisect each other. Find the whole diagonal. 8 6 A fguilbert B Find AB

2 6 + 2 8 = 2 c shortcut 3 - 4 - 5 6 - 8 - 10 8 10 A 6 fguilbert B Find AB

Now find AB. 10/2 = 5 8 10 A 6 fguilbert B B Find AB

Can these numbers form a right triangle? 4, 6, 8 2 4 + 2 6 2 8 Is = Is 16 + 36 = 64 ? fguilbert

Can 9, 15, 12 form a right triangle? Be sure to choose the largest # for c. Is 2 9 2 12 + = 81 + 144 = 225 fguilbert 2 15

x 3 4 w 3 5 What kind of figure is this? y 5 How long is xy ? 1 st Find wy. XY = 6 wy = 3 shortcut? fguilbert

Quote for the day One is not born into the world to do everything but to do something. Henry Thoreau. David Thoreau fguilbert