Download - Lesson 4.4 Angle Properties pp. 135-141
![Page 1: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/1.jpg)
Lesson 4.4Angle Properties
pp. 135-141
Lesson 4.4Angle Properties
pp. 135-141
![Page 2: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/2.jpg)
Objectives:1. To identify linear pairs and
vertical, complementary, and supplementary angles.
2. To prove theorems on related angles.
Objectives:1. To identify linear pairs and
vertical, complementary, and supplementary angles.
2. To prove theorems on related angles.
![Page 3: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/3.jpg)
A linear pair is a pair of adjacent angles whose noncommon sides form a straight angle (are opposite rays).
A linear pair is a pair of adjacent angles whose noncommon sides form a straight angle (are opposite rays).
DefinitionDefinitionDefinitionDefinition
AA BB CC
DD
![Page 4: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/4.jpg)
Vertical angles are angles adjacent to the same angle and forming linear pairs with it.
Vertical angles are angles adjacent to the same angle and forming linear pairs with it.
DefinitionDefinitionDefinitionDefinition
AA BB CC
DD
EE
![Page 5: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/5.jpg)
Two angles are complementary if the sum of their measures is 90°.
Two angles are supplementary if the sum of their measures is 180°.
Two angles are complementary if the sum of their measures is 90°.
Two angles are supplementary if the sum of their measures is 180°.
DefinitionDefinitionDefinitionDefinition
![Page 6: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/6.jpg)
23°23°67°67°
TT FF XX
YY
CC
CFY and YFX are complementaryCFY and YFX are complementary
![Page 7: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/7.jpg)
23°23°157°157°
TT FF XX
YY
CC
TFY and YFX are supplementaryTFY and YFX are supplementary
![Page 8: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/8.jpg)
Theorem 4.1All right angles are congruent.
Theorem 4.1All right angles are congruent.
![Page 9: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/9.jpg)
STATEMENTS REASONS
A and B are Givenright angles
12. mA = 90° 12. _______________mB = 90°
13. mA = mB 13. _______________
14.A B 14. _______________
STATEMENTS REASONS
A and B are Givenright angles
12. mA = 90° 12. _______________mB = 90°
13. mA = mB 13. _______________
14.A B 14. _______________
Def. of rt. angleDef. of rt. angle
SubstitutionSubstitution
Def. of anglesDef. of angles
![Page 10: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/10.jpg)
Theorem 4.2If two angles are adjacent and supplementary, then they form a linear pair.
Theorem 4.2If two angles are adjacent and supplementary, then they form a linear pair.
![Page 11: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/11.jpg)
Theorem 4.3Angles that form a linear pair are supplementary.
Theorem 4.3Angles that form a linear pair are supplementary.
![Page 12: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/12.jpg)
Theorem 4.4If one angle of a linear pair is a right angle, then the other angle is also a right angle.
Theorem 4.4If one angle of a linear pair is a right angle, then the other angle is also a right angle.
![Page 13: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/13.jpg)
Theorem 4.5Vertical Angle Theorem. Vertical angles are congruent.
Theorem 4.5Vertical Angle Theorem. Vertical angles are congruent.
![Page 14: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/14.jpg)
Theorem 4.6Congruent supplementary angles are right angles.
Theorem 4.6Congruent supplementary angles are right angles.
![Page 15: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/15.jpg)
Theorem 4.7Angle Bisector Theorem. If
AB bisects CAD, then mCAB = ½mCAD.
Theorem 4.7Angle Bisector Theorem. If
AB bisects CAD, then mCAB = ½mCAD.
![Page 16: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/16.jpg)
Practice: If the mA = 58°, find the measure of the supplement of A.
Practice: If the mA = 58°, find the measure of the supplement of A.
![Page 17: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/17.jpg)
Practice: If the mA = 58°, find the measure of the complement of A.
Practice: If the mA = 58°, find the measure of the complement of A.
![Page 18: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/18.jpg)
Practice: If the mA = 58°, find the measure of an angle that makes a vertical angle with A.
Practice: If the mA = 58°, find the measure of an angle that makes a vertical angle with A.
![Page 19: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/19.jpg)
Practice: If the mA = 58°, find the measure of an angle that makes a linear pair with A.
Practice: If the mA = 58°, find the measure of an angle that makes a linear pair with A.
![Page 20: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/20.jpg)
Practice: If the mA = 58°, find the measures of the angles formed when A is bisected.
Practice: If the mA = 58°, find the measures of the angles formed when A is bisected.
![Page 21: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/21.jpg)
Homeworkpp. 137-141Homeworkpp. 137-141
![Page 22: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/22.jpg)
►A. ExercisesmAGF = 40°; mBGC = 50°; mAGE = 90°; mEGD = 90°.7. Name two pairs
of supplementaryangles.
►A. ExercisesmAGF = 40°; mBGC = 50°; mAGE = 90°; mEGD = 90°.7. Name two pairs
of supplementaryangles.
A
G
B
CD
E
F
![Page 23: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/23.jpg)
►A. ExercisesmAGF = 40°; mBGC = 50°; mAGE = 90°; mEGD = 90°.9. What is mFGE?
►A. ExercisesmAGF = 40°; mBGC = 50°; mAGE = 90°; mEGD = 90°.9. What is mFGE?
A
G
B
CD
E
F
![Page 24: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/24.jpg)
►B. ExercisesGive the reason for each step in the proofs below.18-22. Theorem 4.3Angles that form a linear pair are supplementary.Given: PAB and BAQ form a linear pairProve: PAD and BAQ are supplementary
►B. ExercisesGive the reason for each step in the proofs below.18-22. Theorem 4.3Angles that form a linear pair are supplementary.Given: PAB and BAQ form a linear pairProve: PAD and BAQ are supplementary
![Page 25: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/25.jpg)
■ Cumulative ReviewReview properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?41. Addition property of
■ Cumulative ReviewReview properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?41. Addition property of
![Page 26: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/26.jpg)
■ Cumulative Review Review properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?42. Multiplication property of
■ Cumulative Review Review properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?42. Multiplication property of
![Page 27: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/27.jpg)
■ Cumulative ReviewReview properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?43. Reflexive property of
■ Cumulative ReviewReview properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?43. Reflexive property of
![Page 28: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/28.jpg)
■ Cumulative ReviewReview properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?44. Transitive property of
■ Cumulative ReviewReview properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?44. Transitive property of
![Page 29: Lesson 4.4 Angle Properties pp. 135-141](https://reader036.vdocuments.net/reader036/viewer/2022062410/56815739550346895dc4e073/html5/thumbnails/29.jpg)
■ Cumulative ReviewReview properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?45. Why is not an equivalence
relation?
■ Cumulative ReviewReview properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?45. Why is not an equivalence
relation?