1. OPENING ACTIVITY
GEOMETRY JEOPARDY

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

3. What are complementary angles?
What are supplementary angles?

4. 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 =
 ABD and  CBD are
COMPLEMENTARY ANGLES

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

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

7. 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°.

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

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

10. Chapter 2: Angle Relationships
Topic: Angle Pairs (continuation)

11. Objectives Enumerate the different kinds of angle pairs
Define each kind of angle pair;
Identify & Illustrate the different kinds of angle pairs, clearly showing their relations.

12. 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.

13. Introduction
Relationship is very important.
- relationship to your fellow students.
- relationship to our friends, neighbors, & other people.

14. We MUST learn to value relationships.
Introduction
Relationship to our family.
Relationship to God.
We MUST learn to value relationships.

15. “ No man is an island. No man can stand alone”
As the saying goes,
“ No man is an island. No man can stand alone”

16. Look at this figure… Adjacent angles. 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. R
. S D
. A P Q

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

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

19. 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

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

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

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

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

24. 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”

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

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

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

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

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

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

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

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

33. Vertical Angles
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 D A P B C

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

35. Vertical Angles Theorem
Vertical angles are congruent.

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

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

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

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

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

41. STUDENT ACTIVITY

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

43. “Linear pair of angles are supplementary” Vertical angles Theorem
State the following:
Linear pair postulate
“Linear pair of angles are supplementary”
Vertical angles Theorem
“Vertical angles are congruent”

44. QUIZ
Get ¼ sheet of paper

45. 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.

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

47. ASSIGNMENT A. Copy & answer the following. Show your solution .
¼ sheet of paper

48. Find the value of x. 1.
2x + 10
4x – 20

49. Find the value of x. 2.
2x - 5
x + 35

50. ASSIGNMENT B. DEFINE THE FOLLOWING: - PERPENDICULAR LINES
- PERPENDICULAR BISECTOR
- EXTERIOR ANGLE OF A TRIANGLE
NOTE:
Write your answer in your notebook

51. B. Solve the following
The supplement of a certain angle is four times larger than its complement. What is the measure of the angle?

52. Find the value of x. 3. 4x
5 x x

53. Find the value of x.
4..
3x-5
2x + 10

54. Find the value of x.

55. B. Solve the following
Two complementary angles are on the ratio 1 : 4. What is the measure of the larger angle?

56. Solution Therefore, the measure of the larger angle is 4 ( 18 ) or 72.
Let x = the measure of the smaller angle
4x = the measure of the larger angle
X + 4x = 90
5x = 90
X = 18
Therefore, the measure of the larger angle is 4 ( 18 ) or 72.

57. SOLVE AND CHECK Solution:
The measure of one of two complementary angles is 15 less than twice the measure of the other. Find the measure of each angle.
Solution:
Let x = measure of the first angle
2x – 15 = measure of the second angle.

58. Solution: X + 2x – 15 = 90 (def. of complementary angles) 3x = 105
x = 35 ( measure of the 1st )
2x -15 = 55 (measure of the 2nd )

59. 55 is 15 less than twice 35. the sum of 35 and 55 is 90.
The measure of one of two complementary angles is 15 less than twice the measure of the other. Find the measure of each angle.
Check:
55 is 15 less than twice 35. the sum of and 55 is 90.