6.5 Pythagorean Theorem

Remember Right Triangles

hypotenuse leg leg

Hypotenuse: Always the side across from the right angle leg leg

Hypotenuse: Always the longest side leg leg

Now let’s look at the 2 leg lengths and the hypotenuse length.

Here it is …

a2 + b2 = c2 Pythagorean Theorem

leg2 + leg2 = hypotenuse2 Pythagorean Theorem

Problem # 1 Hypotenuse = ? Leg= 3 Leg = 4

a2 + b2 = c2 32 + 42 = c2 c = ? a = 3 b =4 25 = c2 5 = c

c = 5 3 4 32 + 42 = 52

Try Another Problem

a2 + b2 = c2 Pythagorean Theorem

leg2 + leg2 = hypotenuse2 Pythagorean Theorem

Problem # 2 c = ? a= 5 B = 12

a2 + b2 = c2 52 + 122 = c2 c = ? a = 5 b =12 169 = c2 13 = c

52 + 122 = 132 13 5 12

Figure out the hypotenuse (c) Let’s try another one where you are given the 2 legs (a, b) Figure out the hypotenuse (c)

a2 + b2 = c2 Pythagorean Theorem

leg2 + leg2 = hypotenuse2 Pythagorean Theorem

Problem # 3 c = ? a= 9 B = 12

a2 + b2 = c2 92 + 122 = c2 c = ? a = 9 b =12 225 = c2 15 = c

92 + 122 = 152 15 9 12

Figure out the other leg (b) Let’s try another one where you are given t 1 leg (a) & the hypotenuse (c) Figure out the other leg (b)

Problem # 4 B = ? A = 2 C =4 What is the value of b?

b 2 4 22 + b2 = 42 b2 = 12 4 + b2 = 16

b 2 4

Now try some problems on your own.