What is a right triangle?

It is a triangle which has an angle that is 90 degrees.

The two sides that make up the right angle are called legs.

The side opposite the right angle is the hypotenuse.

leg

leg

hypotenuse

right angle

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• Wizard of OZ

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Find the length of the hypotenuse if1. a = 12 and b = 16.

122 + 162 = c2

144 + 256 = c2

400 = c2

Take the square root of both sides.

20 = c

2400 c

52 + 72 = c2

25 + 49 = c2

74 = c2

Take the square root of both sides.

8.60 = c

Find the length of the hypotenuse if2. a = 5 and b = 7.

274 c

Find the length of the leg, to the nearest hundredth, if

3. a = 4 and c = 10.42 + b2 = 102

16 + b2 = 100Solve for b.

16 - 16 + b2 = 100 - 16b2 = 84

b = 9.17

2 84b

Find the length of the missing side given a = 4 and c = 5

1. 1

2. 3

3. 6.4

4. 9

What are Pythagorean Triples?

• Three integers that make the equation a2 + b2 = c2 true are called Pythagorean Triples.

• The numbers 3, 4 and 5 are a very famous Pythagorean Triple.

a2 + b2 = c2

32 + 42 = 52

9 + 16 = 25

5, 12, 13Another common

triple

Practice: Are they Pythagorean Triples?

• 1) yes or no? 2) yes or no?

9 + 64 = 7373 = 73

Since this is true, the triangle is a right triangle!! If it was not true, it

would not be a right triangle.

Sides: , 3, and 832 + 82 = ( ) 2

7373

Pythagorean Inequality Theorem

a & b are the legs

c is the hypotenuse

a2 + b2 = c2

c

a

b

Pythagorean Inequalities:

c2 > a2 + b2 - - - Triangle is obtuse

c2 < a2 + b2 - - - Triangle is acute

Pythagorean Inequalities

The following triples represent the side lengths of a triangle. Determine whether the triangle is right, acute or obtuse.

1. 5, 9, 12

2. 7, 24, 26

3. 13, 15, 17

4. 3, 4, 5

5. 25, 25, 30

Obtuse

Obtuse

Acute

Right

Acute