Corollary to the Triangle Exterior Angle Theorem:

The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.

2

3

1

m<1 > m<2 and m<1 > m<3

m<2 = m<1 by the Isosceles Triangle Theorem. Explain why m<2 > m>3.

2

1

4

3

m<1 > m<3 + m<4 because<1 is the exterior angle, som<1 > m<3.

By substitution property, m< 2 > m<3,since m<2 = m<1.

If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.

X

Y

Z14

1211

<Y is the largest angle.

A landscape architect is designing a triangular deck. She wants to place benches in the two larger corners. Which corners have the larger angles?

21ft

27ft

18ft

A

B

C

<B and <A are the larger angles, <C is the smallest.

If two sides of a triangle are not congruent, then the longer side lies opposite the larger angle.

X

Y

Z

48

98

34

XZ is the longest side.

Which side is the shortest?

52 62

66

U

T

V

TV is the shortest side.

4060

X

Y

Z

80

YZ is the shortest side

Triangle Inequality Theorem:The sum of the lengths of any two sides of

a triangle is greater than the length of the third side.

a

b

c a + b > c

b + c > a

c + a > b

Can a triangle have sides with the given lengths?

3ft, 7ft, 8ft

3cm, 6cm, 10cm

Yes, 3 + 7 = 10 and 10 > 8

No, 3 + 6 = 9 and 9 is not greater than 10

Can a triangle have sides with the given lengths?

2m, 7m, 9m

4yd, 6yd, 9yd

No, 2 + 7 = 9, and 9 is not greater than 9

Yes, 4 + 6 = 10 and 10 is greater than 9

A triangle has side lengths of 8cm and 10cm. Describe the possible lengths of the third side.

The value of the third side must be greaterThan 2 and less than 18.(x > 2 and x < 18)

2cm < x < 18cm

To answer this kind of question, add the numbers together andSubtract the small number from the larger number.

8 + 10 = 18 10 – 8 = 2

A triangle has side lengths of 3in and 12in. Describe the possible lengths of the third side.

9in < x < 15in

To answer this kind of question, add the numbers together andSubtract the small number from the larger number.

3 + 12 = 15 12 – 3 = 9

The value of the third side must be greaterThan 9 and less than 15. (x > 9 and x < 15)

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