The Pythagorean Theorem The Pythagorean Theorem For any

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The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem “For any right triangle, the sum of the areas of the

The Pythagorean Theorem “For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger. ” a 2 + b 2 = c 2 9/25/2020 2

What is the Pythagorean Theorem used for? • to find the length of a

What is the Pythagorean Theorem used for? • to find the length of a missing side in a right triangle n 5 4

Pythagorean Theorem Formula 2 • a + a and b represent the legs 2

Pythagorean Theorem Formula 2 • a + a and b represent the legs 2 b = 2 c c represents the hypotenuse

c a hypotenuse leg b leg

c a hypotenuse leg b leg

Important bits of information • The Pythagorean Theorem can only be used on a

Important bits of information • The Pythagorean Theorem can only be used on a right triangle. • The legs are always the sides adjacent (next to) the 90 degree angle. • It does not matter which leg is a and which leg is b. • c is always the hypotenuse (the slant)

What is the length of the hypotenuse in the triangle below? 2 a +

What is the length of the hypotenuse in the triangle below? 2 a + 2 b = 2 c h 2 4

Plug in the value for each variable in the formula.

Plug in the value for each variable in the formula.

What is the length of the hypotenuse in the triangle below? h 2 2

What is the length of the hypotenuse in the triangle below? h 2 2 a + b = c 2 2 + 2 4 = 2 h 4 + 16 = h 2 20 = h 2 4

What is the length of the hypotenuse in the triangle below? a 2 b

What is the length of the hypotenuse in the triangle below? a 2 b 2 + = 22 + 42 = h 2 4 + 16 = h 2 20 = h ~ h 4. 47 ~ c 2 h 2 4

Try this one. . . Find the hypotenuse of the right triangle below? 4

Try this one. . . Find the hypotenuse of the right triangle below? 4 6 h

Find the hypotenuse of the right triangle below? 4 a 2 + b 2

Find the hypotenuse of the right triangle below? 4 a 2 + b 2 = c 2 42 + 62 = h 2 16 + 36 = h 2 52 = h 7. 21 = h 6 h

Try this one. . . What is the length of the missing leg in

Try this one. . . What is the length of the missing leg in the triangle below? 2 a + 2 b = 2 c 5 3 x

Find the hypotenuse of the right triangle below? a 2 + b 2 =

Find the hypotenuse of the right triangle below? a 2 + b 2 = c 2 32 + x 2 = 52 9 + x 2 = 25 -9 - 9 x 2 = 16 16 x=4 5 3 x

Ladder Problem A ladder leans against a second-story window of a house. If the

Ladder Problem A ladder leans against a second-story window of a house. If the ladder is 25 meters long, and the base of the ladder is 7 meters from the house, how high is the window? 9/25/2020 15

Ladder Problem Solution • First draw a diagram that shows the sides of the

Ladder Problem Solution • First draw a diagram that shows the sides of the right triangle. • Label the sides: – Ladder is 25 m – Distance from house is 7 m • Use a 2 + b 2 = c 2 to solve for the missing side. Distance from house: 7 meters 9/25/2020 16

Ladder Problem Solution 72 + b 2 = 252 49 + b 2 =

Ladder Problem Solution 72 + b 2 = 252 49 + b 2 = 625 b 2 = 576 b = 24 m How did you do? 17