4.9 Pythagorean Theorem4.9 Pythagorean Theorem

Standard: MG 3.3

Objective: Find the missing side of a right triangle.

Start Square it Root it Result

233 9 9 3 3

255 25 25 5 5

299 81 81 9 9

Square and Square RootsSquare and Square Roots

Simplify each root below and identify as a positive root or a negative root.

1) 49

2) 25

3) 144

4) 16

7

5

12

4

6

positive root

positive root

positive root

positive root

negative root

36)5

Applies to Right Triangles Only!

leg

leg

hypotenusea

b

c

2 2 2(leg) (leg) (hypotenuse) 2 2 2a b c

9.3 PYTHAGOREAN THEOREM9.3 PYTHAGOREAN THEOREM

Find the missing side of the right triangle in the 1 centimeter grid below.

0 1 2 3 4 5 6 7 8 9 10 11 12 13

8

6

0 1

2

3 4

5

6

7

2 2 2a b c

x 2 2 26 8 x

236 64 x 2100 x

100 or 100 x

10 x

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Find the missing side of the right triangle in the 1 centimeter grid below.

0 1 2 3 4 5 6 7 8 9 10 11 12 13

12

5

2 2 2a b c x 2 2 25 12 x

225 144 x 2169 x

169 or 169 x

13 x

0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 8 9 10 11 12 13

Find the missing side of the right triangle in the 1 centimeter grid below.

0 1 2 3 4 5 6 7 8 9 10 11 12 13

74

0 1 2 3 4 5 6 7

2 2 2a b c

x

2 2 24 7 x 216 49 x 265 x

65 or 65 x

x 65 8.1 cm

0 1 2

3 4 5

6 7

8 9 10 11 12 13

Find the length of the diagonal for a rectanglethat measures 3 inches by 4 inches.

3 in.

4 in.

x

2 2 2a b c 2 2 23 4 x

29 16 x 225 x

25 x

5 x

x 5 inches

Find the HypotenuseFind the Hypotenuse

• To find the To find the hypotenuse, solve for hypotenuse, solve for c.c.

1)

2) a = 3, b = 4, find c.

Example: Find a legExample: Find a leg

• You will not always solve for the hypotenuse (c). Sometimes you will have to find a leg (a or b).

• Example: a2 + b2 = c2

62 + b2 = 102

b2 = 102 - 62

√b2 = √(102 - 62)

b = 8

Example: Find a legExample: Find a leg

• To find a leg, solve To find a leg, solve for a or b.for a or b.

1)

2) b = 30, c = 34

1312

b

Practice: Pythagorean TheoremPractice: Pythagorean Theorem