angle pairs.ppt

geometry

1. Angles Pairs

2. To denote the measure of an angle we write an
“m”in front of the symbol for the angle.
Here are some common angles and their measurements.
2
1 2
3
41 45m   2 90m   3 135m   4 180m  
Review

3. Congruent Angles
•So, two angles are congruent if and only if they have the same
measure.
•So, The angles below are congruent.
3 if and only if .A B m A m B     
Means
Congruent
Means Equal
Review

4. Perpendicular Lines
•Two lines are perpendicular if they
intersect to form a right angle.
See the diagram.
•Suppose angle 2 is the right angle.
Then since angles 1 and 2 are
supplementary, angle 1 is a right
angle too. Similarly, angles 3 and
4 are right angles.
•So, perpendicular lines intersect
to form fourright angles.
4
1
2
34

5. Perpendicular Lines
•The symbol for perpendicularity is
•So, if lines m and nare perpendicular, then we write . .mn
m
nmn

6. Adjacent Angles
Adjacent angles share a common vertex and one common side.
Adjacent angles are “side by side”
and share a common ray.
45º
15º

7. Adjacent Angles
These are examples of adjacent angles.
55º
35º
50º130º
80º
45º
85º
20º

8. Adjacent Angles
These angles are NOTadjacent.
45º55º
50º
100º
35º
35º

9. Vertical Angles
•Two angles formed by intersecting lines and have no
sides in common but share a common vertex.
•Are congruent.
When 2 lines
intersect, they
make vertical
angles.
75º
75º
105º
105º
Commo
n Vertex

10. Vertical
angles are
opposite
one
another.
75º
75º
105º
105º
Vertical Angles

11. Vertical
angles are
opposite
one
another.
Vertical Angles
75º
75º
105º
105º

12. Vertical angles are congruent
(equal).
30º150º
150º
30º
Vertical Angles

13. Vertical Angles
1 4
Two angles that are opposite angles.
Vertical angles are congruent.
12
34
56
78
2 3
5 8,
6 7
Name the Vertical Angles

14. Supplementary Angles
Add up to 180º.
60º120º
40º
140º
Adjacent and
Supplementary Angles

15. Supplementary Angles
•Two angles are supplementaryif their measures add up to
•If two angles are supplementary each angle is the supplementof
the other.
•If two adjacent angles together form a straight angle as below,
then they are supplementary.
15180 .
121 and 2 are
supplementary


16. Complementary Angles
Add up to 90º.
70º
20º
20º
70º
Adjacent and
Complementary Angles

17. Complementary Angles
•Two angles are if their measures add upcomplementaryto
•If two angles are complementary, then each angle is called the complement
of the other.
•If two adjacent angles together form a right angle as below, then they are
complementary.
1790 .
1
2
A
B
C1 and 2 are
complementary
if is a
right angle
ABC



18. Supplementary vs.
Complementary
How do I remember?The way I remember is this:
•C comes before S in the alphabet.
•90 comes before 180 when I count.
•Complementary is 90, Supplementary is 180.

19. Guess Who?
•I am an angle.

20. Guess Who?
•I am an angle.
•I have 180°

21. Guess Who?
•I am an angle.
•I have 180°
•I look like this:

22. Guess Who?
•I am an angle.
•I have 180°
•I look like this:
Supplementary Complementary

23. Guess Who?
•I am two adjacent angles.

24. Guess Who?
•I am two adjacent angles.
•I look like an “L” with a line in the middle.

25. Guess Who?
•I am two adjacent angles.
•I look like an “L” with a line in the middle.
•I add up to 90°
•I look like this:

26. Guess Who?
•I am two adjacent angles.
•I look like an “L” with a line in the middle.
•I add up to 90°
•I look like this:
Complementary
Supplementary

27. Guess Who?
Complementary
Supplementary

28. Guess Who?
Complementary
Supplementary

29. Review
•Complementary angles are…….

30. Review
•Complementary angles
are…….

31. Review
•Supplementary Angles
are…..

32. Practice Time!

33. Find the missing angle
55
x
I know that these angles are
complementary.
They must add up to 90°
So……
90 –55 = 35
The missing angle is 35

34. You try.
20
x
Are they
supplementary or
complementary?
Find the missing
side.

35. You try.
20
x
Are they
supplementary or
complementary?
complementary
Find the missing
side.
90 –20 = 70
The missing angle
Is 70

36. One More
50
x

37. Find the missing angle
120
x
I know these are supplementary angles.
Supplementary angles add up to 180.
The given angle is 120. So…..
180 –120 = 60
The missing angle is 60

38. Find the missing angle
130
x
What kind of angles?
What’s the missing angle?

39. Find the missing angle
130
x
What kind of angles?
Supplementary
What’s the missing angle?
Adds up to 180, so…..
180 –130 = 50

40. Find the missing angle
x
30
Do this one on your own.

41. Directions:
Identify each pair of angles as
adjacent, vertical, supplementary,
complementary,
or none of the above.

42. #1
60º
120º

43. #1
60º
120º
Supplementary Angles
Adjacent Angles

44. #2
60º
30º

45. #2
60º
30º
Complementary Angles

46. #3
75º
75º

47. #3
75º
75º
Vertical Angles

48. #4
60º
40º

49. #4
60º
40º
None of the above

50. #5
60º
60º

51. #5
60º
60º
Vertical Angles

52. #6
45º135º

53. #6
45º135º
Supplementary Angles
Adjacent Angles

54. #7
65º
25º

55. #7
65º
25º
Complementary Angles
Adjacent Angles

56. #8
50º
90º

57. #8
50º
90º
None of the above

58. Directions:
Determine the missing angle.

59. #1
45º?º

60. #1
45º135º

61. #2
65º
?º

62. #2
65º
25º

63. #3
35º
?º

64. #3
35º
35º

65. #4
50º
?º

66. #4
50º
130º

67. #5
140º
?º

68. #5
140º
140º

69. #6
40º
?º

70. #6
40º
50º

71. ACTIVITY 1: LET’S PRACTICE!
Direction: Write True if the statement is correct but if it’s False,
change the
underlined word or number to make the whole statement true.
__________1. Complementary angles measure 180 degree.
__________2. The sum of the measures of angles at a point is 360
degree.
__________3. If two angles form a linear pair, then they are
complementary.
__________4. The measures of adjacent angles are congruent.
__________5. If the sum of two adjacent angles is 180degree, then
these angles form a linear pair.

74. Valuing
REFLECTION: (Journal Writing)
Take a look around you. There are many things
that works in pair. Give one example of it and
compose a song pertaining to the importance of
working by pair in real life.