A REVIEW ABOUT COMPLEMENTARY ANGLES & SUPPLEMENTARY ANGLES

1. A REVIEW ABOUT COMPLEMENTARY ANGLES & SUPPLEMENTARY ANGLES Topic: Angle Pairs

2. What are complementary angles? • What are supplementary angles?

3. Consider the following: Complementary Angles -Are two angles that together make a right angle. The measures of the two angles must add up to 90°. A D 30º 60º B C m ABC = m ABD + m CBD 90 = 30 + 60 ABD and CBD are COMPLEMENTARY ANGLES

4. Consider the following: R Two 45º angle are Complementary. RPD and QPD are Complementary angles. D 45º 45º P Q

5. Consider this figure Can we say that B and  Q are Complementary angles? B and Q are Complementary angles. • B is a complement to Q.  Q is a complement to  B. 70º Q 20º B

6. Supplementary Angles • Are two angles that together form one-half of a complete rotation—that is, 180°. • The measures of two supplementary angles, therefore, must add up to 180 when added together. • The supplementary angle of a 50° angle, for example, is a 130°.

7. Consider the following: What can you say about the angle sum measure of  RPD and  QPD ? mRPD + m QPD = 180. Therefore,  RPD and  QPD are supplementary angles. D 145º 35º R P Q

8. Another illustration: m R + m  P = 180. •  R and  P are supplementary angles. •  R is a supplement to  P .  P is a supplement to  R. 150º 30º R P

9. Introduction • Relationships exist between angles. • If two angles have the same measure, then they are CONGRUENT. • For example, if mA = 50 and mB = 50, then A  B . • By the sum of their measures, relations can be established.

10. Look at this figure… R Consider RPD and QPD. - share a common vertex(P), • Share a common side (segment PD) • but no interior points in common.  RPD and  QPD are Adjacent angles. . S D . A P Q

11. ADJACENT ANGLES • Are angles meeting at a common vertex (corner) and sharing a common side but NO interior points in common.

12. Consider this figure R  RPD and  QPD are Adjacent angles & complementary. . S D . A P Q

13. How about the other pairs of angles in the figure? Like , • RPD and QPR ? • QPD and QPR ? Are these pairs of angles Adjacent or not ? why? These pairs of angle are NON – ADJACENT ANGLES. . S R D . A P Q

14. Consider this figure Can we say that B and  Q are Complementary? Adjacent or non-adjacent? B and Q are Complementary angles BUT non- adjacent angles. 70º Q 20º B

15. Another illustration: mR + m P = 180. R and  P are supplementary angles and non - adjacent angles. 150º 30º R P

16. Consider the following:  RPD and  QPD are supplementary angles and Adjacent angles. D 145º 35º R P Q

17. Consider the following: What can you say about ray PR & ray PQ of RPD & QPD? They are non- common sides & opposite rays.  RPD and  QPD are LINEAR PAIR of angles. D 145º 35º R P Q

18. Definition of LINEAR PAIR • Are TWO adjacent angles and whose non common sides are opposite rays. LINEAR PAIR POSTULATE States that “ Linear pair of angles are supplementary”

19. In the figure:  RPD and  QPD are LINEAR PAIR of angles and supplementary. D 145º 35º R P Q

20. In the figure, name & identify linear pair of angles. • APC and BPC, APD and APC APD and DPB, DPD and BPC are LINEAR PAIR of angles. D A P B C

21. REMEMBER THIS….. • LINEAR PAIR of angles are adjacent and supplementary.

22. In the figure, we can write an equation. Like, • mAPC +mBPC = 180 • mAPD + mAPC = 180 • mAPD + mDPB = 180 • mDPD + mBPC = 180 D A P C B

23. In the figure, if mAPD = 120. . What is the measure of the other angles? • mAPC +mBPC = 180 • mAPD + mAPC = 180 • mAPD + mDPB = 180 • mDPD + mBPC = 180 D A P C B

24. In the figure, if mAPD = 120. . What is the measure of the other angles? • mAPD+ mAPC = 180 (linear pair postulate) • 120 + mAPC = 180 ( by substitution) • mAPC = 60( by subtraction) D 120° A 60° 60° P 120° C B

25. In the given figure, what are non- adjacent angles? • APD and BPC • APC and BPD • These non-adjacent angles are also called vertical angles. D 120° A 60° 60° P 120° C B

26. Vertical Angles • In the figure, APC and BPD, APD and BPC are vertical angles. D A P B C

27. Vertical Angles D A • ARE TWO NON ADJACENT ANGLES formed by two intersecting lines. • APC and BPD, APD and BPC are NON ADJACENT angles. • Line AB and line CD are two intersecting lines P B C

28. What can you say about the measures of the vertical angles? • mAPD= mBPC • mAPC = mBPD D 120° A 60° 60° P 120° C B APD and BPC APC and BPD These non-adjacent angles are also called vertical angles.

29. Fixing skills A B • In the given figure, APB and CPD are right angles. Name all pairs of: • Complementary angles. 1 2 3 4 P 6 5 7 8 C D ANSWERS: 3 AND 4 5 AND 6

30. Fixing skills A B • In the given figure, APB and CPD are right angles. Name all pairs of: 2. Supplementary angles. 1 2 3 4 P 6 5 7 8 C D ANSWERS: 1 AND 2 7 AND 8

31. Fixing skills A B • In the given figure, APB and CPD are right angles. Name all pairs of: 3. Vertically opposite angles. 1 2 3 4 P 6 5 7 8 C D ANSWERS: CPD and BPA APC and DPB 3 AND 6 5 AND 4

32. Fixing skills A B • In the given figure, APB and CPD are right angles. Name all pairs of: 4. Linear pair of angles. 1 2 3 4 P 6 5 7 8 C D ANSWERS: 1 AND 2 7 AND 8

33. Fixing skills A B • In the given figure, APB and CPD are right angles. Name all pairs of: 5.Adjacent angles. 1 2 3 4 P 6 5 7 8 C D 1 AND 2 3 AND 4 5 AND 6 7 AND 8 ANSWERS:

34. STUDENT ACTIVITY

35. Define the following pairs of angles: • Adjacent angles • Linear pair of angles • Vertical angles

36. State whether each of the following is TRUE or FALSE. • TWO ADJACENT RIGHT ANGLES ARE SUPPLEMENTARY. • ALL SUPPLEMENTARY ANGLES ARE ADJACENT. • SOME SUPPLEMENTARY ANGLES ARE LINEAR PAIR.

37. State whether each of the following is TRUE or FALSE. 4. TWO VERTICAL ANGLES ARE ALWAYS CONGRUENT. 5. ALL RIGHT ANGLES ARE CONGRUENT.