Lesson 7.3Exterior Angles and

Inequalitiespp. 273-278

Lesson 7.3Exterior Angles and

Inequalitiespp. 273-278

Objectives:1. To review the real number

properties of inequality and apply them to exterior angles.

2. To prove and apply the relation between an exterior angle and the two remote interior angles.

Objectives:1. To review the real number

properties of inequality and apply them to exterior angles.

2. To prove and apply the relation between an exterior angle and the two remote interior angles.

An exterior angle of a triangle is an angle that forms a linear pair with one of the angles of the triangle.

An exterior angle of a triangle is an angle that forms a linear pair with one of the angles of the triangle.

DefinitionDefinitionDefinitionDefinition

11

22 33

4455

66

77 88

99

The remote interior angles of an exterior angle are the two angles of the triangle that do not form a linear pair with a given exterior angle.

The remote interior angles of an exterior angle are the two angles of the triangle that do not form a linear pair with a given exterior angle.

DefinitionDefinitionDefinitionDefinition

AA BB CC

DD

ABD is an exterior angle of BCD.ABD is an exterior angle of BCD.C and D are remote interior angles of ABD.

11

22 33

4455

66

77 88

99

Theorem 7.10Exterior Angle Theorem. The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

Theorem 7.10Exterior Angle Theorem. The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

MM

NN

OO

PP42°42°

87°87°

Find mMNP.Find mMNP.

Theorem 7.11Exterior Angle Inequality. The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.

Theorem 7.11Exterior Angle Inequality. The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.

Practice: Find mABD.Practice: Find mABD.

33°33°110°110°

AA BB CC

DD

70°70°

Practice: Find mWZY.Practice: Find mWZY.

WW

XX YY ZZ

76°76°

52°52°

Practice: Find mWYX.Practice: Find mWYX.

WW

XX YY ZZ

76°76°

128°128°

Homeworkpp. 275-278Homeworkpp. 275-278

►A. ExercisesFind the measure of the indicated angles.1. mA

►A. ExercisesFind the measure of the indicated angles.1. mA

65º65ºBB CC DD

AA

►A. ExercisesFind the measure of the indicated angles.1. mBCA

►A. ExercisesFind the measure of the indicated angles.1. mBCA

65º65ºBB CC DD

AA

►A. ExercisesFind the measure of the indicated angles.1. mACD

►A. ExercisesFind the measure of the indicated angles.1. mACD

65º65ºBB CC DD

AA

►A. ExercisesFind the measure of the indicated angles.5. mONL

►A. ExercisesFind the measure of the indicated angles.5. mONL

LL MM

NN

OO

x - 60ºx - 60º x - 20ºx - 20º

xx

►A. ExercisesFind the measure of the indicated angles.5. mLNM

►A. ExercisesFind the measure of the indicated angles.5. mLNM

LL MM

NN

OO

x - 60ºx - 60º x - 20ºx - 20º

xx

►A. ExercisesFind the measure of the indicated angles.5. mL

►A. ExercisesFind the measure of the indicated angles.5. mL

LL MM

NN

OO

x - 60ºx - 60º x - 20ºx - 20º

xx

►A. ExercisesFind the measure of the indicated angles.5. mM

►A. ExercisesFind the measure of the indicated angles.5. mM

LL MM

NN

OO

x - 60ºx - 60º x - 20ºx - 20º

xx

xx

►A. ExercisesRefer to ABC; give the measure of the exterior angles at each vertex.7. A

►A. ExercisesRefer to ABC; give the measure of the exterior angles at each vertex.7. A

AA

BB

CC

60º60º

80º80º

40º40º

►A. Exercises11. If ABC is equilateral, what is the

measure of an exterior angle?

►A. Exercises11. If ABC is equilateral, what is the

measure of an exterior angle?

60º60º

►B. Exercises13. If an exterior angle at the vertex of

an isosceles triangle measures 78 degrees, what are the measures of the base angles?

►B. Exercises13. If an exterior angle at the vertex of

an isosceles triangle measures 78 degrees, what are the measures of the base angles?

78º78º

►B. Exercises15. If ABCD is a rhombus and C-D-E,

what is the relationship between mEDA and mDAC?

►B. Exercises15. If ABCD is a rhombus and C-D-E,

what is the relationship between mEDA and mDAC?

DD CC

BBAA

►B. Exercises15. If ABCD is a rhombus and C-D-E,

what is the relationship between mEDA and mDAC?

►B. Exercises15. If ABCD is a rhombus and C-D-E,

what is the relationship between mEDA and mDAC?EE DD CC

BBAA

■ Cumulative ReviewHow does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case.24.

■ Cumulative ReviewHow does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case.24.

qq

rr

■ Cumulative ReviewHow does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case.25.

■ Cumulative ReviewHow does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case.25.

bb

cc

aa

■ Cumulative ReviewHow does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case.26.

■ Cumulative ReviewHow does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case.26.

rr

ss

tt

■ Cumulative ReviewHow does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case.27.

■ Cumulative ReviewHow does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case.27.

mm

nn

ll

■ Cumulative ReviewHow does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case.28.

■ Cumulative ReviewHow does each diagram illustrate a method of proving two lines parallel? Identify the parallel lines in each case.28.

hh

pp

gg