5.5 Inequalities in Triangles

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# 5.5 Inequalities in Triangles - PowerPoint PPT Presentation

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. &lt;Y is the largest angle. Comparing Angles.

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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
• 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
• 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
• Which side is the shortest?

T

52

62

U

V

Y

60

Z

40

X

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