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Pythagorean Theorem

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Page 1: Pythagorean Theorem PPT Blog

Pythagorean Theorem

Page 2: Pythagorean Theorem PPT Blog

Parts of a Right Triangle

b

ca

Hypotenuse

Right Triangle

Leg

Leg

Page 3: Pythagorean Theorem PPT Blog

b

ca

Use the sides of the triangle to make a square with equal sides.

35

4

55

5

4

4

4

3

3

3

a = 3b = 4c = 5

Page 4: Pythagorean Theorem PPT Blog

Find the area of each of the squares created…

Side = 3Area = 32 = 9

Side = 4Area = 42 = 16

Side = 5Area = 52 = 25

Page 5: Pythagorean Theorem PPT Blog

b

ca9

16

25

What is the relationship between the area of the 2 smaller squares and the area of the larger square?

Page 6: Pythagorean Theorem PPT Blog

Discovery Activity

We can conclude that the sum of the area of the 2 smaller squares is equal to the area of the larger square.

9 16 25+ =

Page 7: Pythagorean Theorem PPT Blog

Pythagorean Theorem

Years ago, a man named Pythagoras found an amazing fact about triangles: If the triangle had a right angle (90°) and you made a square on each of the three sides, then ... the biggest square had the exact same area as the other two squares put together!

Pythagorean Theorem is: a2 + b2 = c2

Page 8: Pythagorean Theorem PPT Blog

What Pythagoras Discovered!!!

Page 9: Pythagorean Theorem PPT Blog

Pythagorean Theorem

Problems in this unit will not include square shapes but will look like this! b

c ___ + ___ = ____a

Although you do not see the square shapes you will still need to square the sides of the triangle to determine the relationship.

a2 b2 c2

Page 10: Pythagorean Theorem PPT Blog

Pythagorean Theorem

3

4

5

1.) Plug in values of a, b, & c into the formula.

2.) Square values of a, b, c

3.) Add the squares on the left side.

The left and right sides should be equal!

a2 + b2 = c2 __2 + __2 = __2

__ + __ = ____ = __

3 4 5

9 16 25

25 25

Page 11: Pythagorean Theorem PPT Blog

Why is this useful?

• If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. (But remember it only works on right angled triangles!)

Let’s try!!!a

b

?

Page 12: Pythagorean Theorem PPT Blog

Example 1

5 12

25 144

169

169

13

Page 13: Pythagorean Theorem PPT Blog

Example 2

9 15

81 225

81

144

144

12

Page 14: Pythagorean Theorem PPT Blog

Now You Try!!!

Page 15: Pythagorean Theorem PPT Blog

Know Before You Go

Today’s Lesson was on:___________________

Three important things to remember:1.) Write the formula for the Pythagorean Theorem.2.) What is the only type of triangle that the

Pythagorean Theorem will work for?3.) Why is the Pythagorean Theorem useful?