lesson 7.3 exterior angles and inequalities pp. 273-278
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Lesson 7.3 Exterior Angles and Inequalities pp. 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. Definition. - PowerPoint PPT PresentationTRANSCRIPT
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.
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