Chapter 5: Relationships Within Triangles

1
Chapter 5 Relationships Within Triangles

• 5.5
• Inequalities in Triangles

2
Comparison Property of Equality

• If a b c, and c gt 0, then a gt b.

b
a
c
3
Corollary

• 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.

4
Theorem 5-10

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

5
Example 2

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

6
Theorem 5-11

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

7
Example 3

• List the sides of ?TUV in order from shortest to
  longest

8
Example 3a

• List the sides of ?XYZ in order from shortest to
  longest. Explain your reasoning!

9
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.

10
Example 4

• Can a triangle have sides with the given lengths?
• 3 ft, 7 ft, 8 ft
• 3 cm, 6 cm, 10 cm

11
Example 5

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

12
Example 5a

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

13
Homework

• P. 292
• 2-26 EVEN