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4.9 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 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 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 Hypotenuse
• To find the hypotenuse, solve for c.
1)
2) a = 3, b = 4, find c.
Example: Find a leg
• You will not always solve for the hypotenuse (c). Sometimes you will have to find a leg (a or b).
• Example:
Example: Find a leg
• To find a leg, solve for a or b.
1)
2) b = 30, c = 34
1312
b
Practice: Pythagorean Theorem