5.5 Inequalities in Triangles

DOM

Can you figure out the puzzle below???

Domino

Comparison Property of Inequality

Comparison Property of Inequality:If a = b + c, and c > 0, then a > b.

a

b c

Theorem

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.

31 and 21 mmmm

1

3

2

Application

32 mmGiven the figure below, explain why .

21 mm

31 mm

32 mm

Statements Reasons

1.

2.

3.

1.

2.

3.

Theorem

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

. then ,Z If ZmYmXYX

Example

List the angles of the following figure in order from smallest to largest.

Theorem

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

. then ,Am If ACBCBm

Sides of a Triangle

List the sides of the following triangle in order from shortest to longest.

Determine which segment is shortest in the following diagram.

Theorem

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.

XZX YZY YX ZXYZ ZYXZX Y

Theorem

Can a triangle have sides with the given lengths?

a) 7 ft, 3 ft, 8 ft

b) 10 cm, 6 cm, 3 cm

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

5.5 Inequalities in Triangles

HW 5.5: #1-25 (1st column), 32, 33, 35

p.192: #3-4, 11, 22, 24-26ESGGSGEGGEGSSGGE

Can you figure out the puzzle below???

Scrambled Eggs

Proof of Comparison Property of Inequality

Statements Reasons

1.

2.

3.

4.

5.

1.

2.

3.

4.

5.

Given: a = b + c, c > 0

Prove: a > b

c > 0b + c > b + 0

b + c > ba = b + c

a > b

Midterm ReviewGiven the figure below, name the type of angle pairs given.

8 and 3 1)

6 and 4 2)

7 and 1 3)

7 and 2 4)

8 and 5 5)

5 and 4 6)

Midterm ReviewFind . Justify each answer.2 and 1 mm

1)

2)

135°

1

2

Midterm ReviewFind x in the following polygon.

125° 125°x°

Midterm Review

Find the equation of a line parallel to y + 3x = 5 that goes through the point (-3, 5).

Find the equation of a line that goes through the point (-2, 1) and (3,2).