5.3 5.3 Inequalities in One TriangleInequalities in One Triangle

ObjectivesObjectives::• Recognize and apply properties of Recognize and apply properties of

inequalities to the measures of the inequalities to the measures of the angles of a triangle.angles of a triangle.

• Recognize and apply properties of Recognize and apply properties of inequalities to the relationships inequalities to the relationships between the angles and sides of a between the angles and sides of a triangle.triangle.

ConceptConcept

Example 1Example 1

Example 2Example 2

Practice #1Practice #1

A.

B.

C.

D.

A.

B.

C.

D.

Practice #2Practice #2

A.

B.

C.

D.

A.

B.

C.

D.

5 7

835˚80˚

65˚

20˚

75˚ 85˚

5.5

ConceptConcept

What is the largest angle of the given triangle?

B

CA

5.5

5 7

9

Example 3Example 3

Practice #3Practice #3

A. X, T, V

B. X, V, T

C. V, T, X

D. T, V, X

List the angles of ΔTVX in order from smallest to largest.

List the sides from largest to smallest.

5.5

FE

D

110°

46°

A. DE, EF, DF

B. EF, DE, DF

C. DE, DF, EF

D. DF, DE, EF

Practice #4Practice #4

A triangle is formed by three kitchen appliances as shown in the figure. The distances shown are measured in feet. What is wrong with the labels?

5.5

50°

60°

70°

10

6

8

refrigerator

sink

range

Practice #5Practice #5

5.6 5.6 Inequalities in Two TrianglesInequalities in Two Triangles

ObjectivesObjectives::• Apply the Hinge Theorem or its Apply the Hinge Theorem or its

converse to make comparisons in two converse to make comparisons in two triangles.triangles.

• Prove triangle relationships using the Prove triangle relationships using the Hinge Theorem or its converse.Hinge Theorem or its converse.

Think about this…Think about this…

ConceptConcept

Complete the inequality (or equation):

Example 4Example 4

Complete the equation or inequality:3) m<1 ___ m<2 4) MS ____ LS 5) m<1 ____ m<2

Example 4Example 4

Practice #6Practice #6

A. FG > GH

B. FG < GH

C. FG = GH

D. not enough information

A. Compare the lengths of FG and GH.

Practice #7Practice #7

A. mJKM > mKML

B. mJKM < mKML

C. mJKM = mKML

D. not enough information

B. Compare mJKM and mKML.

Practice #8Practice #8

A. Meena’s kite

B. Rita’s kite

Meena and Rita are both flying kites in a field near their houses. Both are using strings that are 10 meters long. Meena’s kite string is at an angle of 75° with the ground. Rita’s kite string is at an angle of 65° with the ground. If they are both standing at the same elevation, which kite is higher in the air?

Warm UpWarm Up

Use the Exterior Angle Inequality Theorem to:

a)List the angles that are greater than m<2

b)List the angles that are less than m<5

c)List the angles that are greater than m<8

Homework QuizHomework Quiz Write down the work and Write down the work and

answer for the following:answer for the following: 1.) pg. 349 #221.) pg. 349 #22

2.) Use the figure at the 2.) Use the figure at the right to determine which right to determine which angle has the greatest angle has the greatest measure.measure.• a) <1, <5, or <6a) <1, <5, or <6• b) <3, <11, or <12b) <3, <11, or <12