Section 5.5

Inequalities in One Triangle

Theorem 5.10

• If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

15

12

A

B

A B

THEOREM 5.11

• If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle

60 o

45 o

Side 1

Side 2Side 1 > Side 2

Write the sides/angles in order from least to greatest.

A

B

C

D

F

E

33

22

15

63

32

Is PQ>8? Is RQ<8?

P

Q

R61

57

8

Exterior Angle Inequality

• The measure of an exterior angle of a triangle is greater then the measure of either of the two nonadjacent interior angles.

1

A

B

<1 is greater than <A

<1 is greater than <B

What are the possible angle measures of <A?

A

42

Triangle Inequality

• The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

BC

A

AB + BC >AC

AC + BC > AB

AB + AC > BC

Is it possible to have a triangle with the given side lengths?

• 3, 8, 3• 6, 7, 12• 9, 5, 11• 8, 12, 20

What are the possible lengths of the third side of the triangle?

• 8, 17, ?

• 12, 18, ?

Write and solve the inequality PQ + QR > PR.

P

Q

R

3x-32x+1

3x+1