1. Lesson 4.4
Angle Properties pp

2. Objectives:
1. To identify linear pairs and vertical, complementary, and supplementary angles.
2. To prove theorems on related angles.

3. Definition
A linear pair is a pair of adjacent angles whose noncommon sides form a straight angle (are opposite rays). A B C D

4. Definition
Vertical angles are angles adjacent to the same angle and forming linear pairs with it. E A B C D

5. Definition
Two angles are complementary if the sum of their measures is 90°.
Two angles are supplementary if the sum of their measures is 180°.

6. 23°
67° T F X Y C
CFY and YFX are complementary

7. C Y
157°
23° T F X
TFY and YFX are supplementary

8. Theorem 4.1
All right angles are congruent.

9. 13. mA = mB 13. _______________ 14. A  B 14. _______________
STATEMENTS REASONS
A and B are Given
right angles
12. mA = 90° 12. _______________
mB = 90°
13. mA = mB 13. _______________
14. A  B 14. _______________
Def. of rt. angle
Substitution
Def. of  angles

10. Theorem 4.2
If two angles are adjacent and supplementary, then they form a linear pair.

11. Theorem 4.3
Angles that form a linear pair are supplementary.

12. Theorem 4.4
If one angle of a linear pair is a right angle, then the other angle is also a right angle.

13. Theorem 4.5
Vertical Angle Theorem. Vertical angles are congruent.

14. Theorem 4.6
Congruent supplementary angles are right angles.

15. Theorem 4.7 Angle Bisector Theorem. If
AB bisects CAD, then mCAB = ½mCAD.

16. Practice: If the mA = 58°, find the measure of the supplement of A.

17. Practice: If the mA = 58°, find the measure of the complement of A.

18. Practice: If the mA = 58°, find the measure of an angle that makes a vertical angle with A.

19. Practice: If the mA = 58°, find the measure of an angle that makes a linear pair with A.

20. Practice: If the mA = 58°, find the measures of the angles formed when A is bisected.

21. Homework pp

22. mAGF = 40°; mBGC = 50°; mAGE = 90°; mEGD = 90°.
►A. Exercises
mAGF = 40°; mBGC = 50°; mAGE = 90°; mEGD = 90°.
7. Name two pairs of supplementary angles. A G B C D E F

23. mAGF = 40°; mBGC = 50°; mAGE = 90°; mEGD = 90°. 9. What is mFGE?
►A. Exercises
mAGF = 40°; mBGC = 50°; mAGE = 90°; mEGD = 90°.
9. What is mFGE? A G B C D E F

24. ►B. Exercises Give the reason for each step in the proofs below.
Theorem 4.3
Angles that form a linear pair are supplementary.
Given: PAB and BAQ form a linear pair
Prove: PAD and BAQ are supplementary

25. ■ Cumulative Review 41. Addition property of 
Review properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?
41. Addition property of 

26. ■ Cumulative Review 42. Multiplication property of 
Review properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?
42. Multiplication property of 

27. ■ Cumulative Review 43. Reflexive property of 
Review properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?
43. Reflexive property of 

28. ■ Cumulative Review 44. Transitive property of 
Review properties of equality and inequality (Sections 3.1, 4.1). What would each property of inequality below be?
44. Transitive property of 

29. ■ Cumulative Review 45. Why is  not an equivalence relation?
Review 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?