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5.5 Inequalities in Triangles. Chapter 5 Relationships Within Triangles. Theorem 5-10. If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side. Y. 11. 12. X. 14. Z. <Y is the largest angle. Comparing Angles.

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5 5 inequalities in triangles

5.5 Inequalities in Triangles

Chapter 5

Relationships Within Triangles

theorem 5 10
Theorem 5-10
  • If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.

Y

11

12

X

14

Z

<Y is the largest angle.

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

A

27ft

C

18ft

21ft

B

theorem 5 11
Theorem 5-11
  • If two sides of a triangle are not congruent, then the longer side lies opposite the larger angle.

Y

98

48

34

X

Z

using theorem 5 11
Using Theorem 5-11
  • Which side is the shortest?

T

52

62

U

V

Y

60

Z

40

X

theorem 5 12
Theorem 5-12
  • 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

b + c > a

c + a > b

c

a

b

triangle inequality theorem
Triangle Inequality Theorem
  • Can a triangle have sides with the given lengths?
  • 3ft, 7ft, 8ft
  • 3cm, 6cm, 10cm
triangle inequality theorem8
Triangle Inequality Theorem
  • Can a triangle have sides with the given lengths?
  • 2m, 7m, 9m
  • 4yd, 6yd, 9yd
finding possible side lengths
Finding Possible Side Lengths
  • A triangle has side lengths of 8cm and 10cm. Describe the possible lengths of the third side.

To answer this kind of question, add the numbers together and

Subtract the small number from the larger number.

finding possible side lengths10
Finding Possible Side Lengths
  • A triangle has side lengths of 3in and 12in. Describe the possible lengths of the third side.

To answer this kind of question, add the numbers together and

Subtract the small number from the larger number.

practice
Practice
  • Pg 277 4 - 27