10.5 - Pythagorean Theorem

Vocab

100

Hypotenuse

The longest leg of a right triangle; opposite the right angle

200

Legs

The sides of a triangle

300

Right triangle

A triangle with one right angle

400

Pythagorean Theorem

a^2 + b^2 = c^2

500

Pythagorean Triplets

Integers that make the Pythagorean Theorem true

Easy Problems

100

a = 15

c = 39

b = ?

b = 36

200

b = 60

c = 75

a = ?

a = 45

300

7, 20, 23

Not a triplet, and does not make the Pythagorean Theorem true (cannot be a right triangle)

400

65, 72, 97

It is a triplet and it does make the Pythagorean Theorem true (can be a right triangle)

500

Which leg is missing from the following triplet:

28, 53

B (the second leg) which is 45

(A could also be an acceptable answer, as they are interchangeable)

Hard Problems

100

8, 31.5, 32.5

Yes, this makes the Pythagorean Theorem true (and therefore can be a right triangle), but IT IS NOT A TRIPLET. Triplets can only be integers, which these are not. 

200

You have a right triangle graphed. Point A is at (5,6). Point B is at (-5, -1). Point C is at (5, -1). Line AB forms the hypotenuse. Find the length of the hypotenuse. 

About 12.21 (rounded to the nearest hundredth)

300

a = x

b = x + 41

c = 85

x = 36

400

a = 12

b = x - 2

c = x

x = 37

500

A right triangle has a hypotenuse of 37 inches. Leg A is 23 inches longer than Leg B. Find the perimeter. 

84 inches