the angle pairs power point presentation

this slide is all about angle pairs

1. 7-1 7-2 Angles PA

2. Measurement of an Angle
2

3. 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.
3
1 2
3
41 45m   2 90m   3 135m   4 180m  

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

5. Types of Angles
•An acuteangle is an angle that measures less than
90 degrees.
•A rightangle is an angle that measures exactly 90
degrees.
•An obtuseangle is an angle that measures more
than 90 degrees.
5
acute right obtuse

6. •A straightangle is an angle that measures 180
degrees. (It is the same as a line.)
•When drawing a right angle we often mark its
opening as in the picture below.
6
straight angle
right angle
Types of Angles

7. 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.
7
1
2
34

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

9. 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

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

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

12. 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
Common
Vertex

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

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

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

16. 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

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

18. 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.
18180 .
121 and 2 are
supplementary


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

20. Complementary Angles
•Two angles are if their measures add
upcomplementaryto
•If two angles are complementary, then each
angle is called the complementof the other.
•If two adjacent angles together form a right
angle as below, then they are complementary.
2090 .
1
2
A
B
C1 and 2 are
complementary
if is a
right angle
ABC



21. 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.

22. Guess Who?
•I am an angle.

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

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

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

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

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

28. 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:

29. 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

30. Guess Who?
Complementary
Supplementary

31. Guess Who?
Complementary
Supplementary

32. Review
•Complementary angles
are…….

33. Review
•Complementary angles
are…….

34. Review
•Supplementary Angles
are…..

35. Practice Time!

36. 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

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

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

39. One More
50
x

40. 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

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

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

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

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

45. #1
60º
120º

46. #1
60º
120º
Supplementary Angles
Adjacent Angles

47. #2
60º
30º

48. #2
60º
30º
Complementary Angles

49. #3
75º
75º

50. #3
75º
75º
Vertical Angles

51. #4
60º
40º

52. #4
60º
40º
None of the above

53. #5
60º
60º

54. #5
60º
60º
Vertical Angles

55. #6
45º135º

56. #6
45º135º
Supplementary Angles
Adjacent Angles

57. #7
65º
25º

58. #7
65º
25º
Complementary Angles
Adjacent Angles

59. #8
50º
90º

60. #8
50º
90º
None of the above

61. Directions:
Determine the missing angle.

62. #1
45º?º

63. #1
45º135º

64. #2
65º
?º

65. #2
65º
25º

66. #3
35º
?º

67. #3
35º
35º

68. #4
50º
?º

69. #4
50º
130º

70. #5
140º
?º

71. #5
140º
140º

72. #6
40º
?º

73. #6
40º
50º

74. Transversal
•Definition:A line that intersects two or more lines in a
plane at different points is called a transversal.
•When a transversal tintersects line nand m, eight angles
of the following types are formed:
Exterior angles
Interior angles
Consecutive interior angles
Alternative exterior angles
Alternative interior angles
Corresponding angles
t
m
n

75. Corresponding Angles
Corresponding Angles:Two angles that occupy
corresponding positions.
75
2 6
12
34
56
78
1 5
3 7
4 8
The corresponding angles are the ones at the same location
at each intersection

76. Angles and Parallel Lines
•If two parallel lines are cut by a transversal, then the
following pairs of angles are congruent.
1.Corresponding angles
2.Alternate interior angles
3.Alternate exterior angles

77. Proving Lines Parallel
•If two lines are cut by a transversal and corresponding
angles are congruent, then the lines are parallel.DC
BA

78. Alternate Angles
•Alternate Interior Angles: Two angles that lie between parallel
lines on opposite sides of the transversal (but not a linear pair).
•Alternate Exterior Angles: Two angles that lie outside parallel
lines on opposite sides of the transversal.
Lesson 2-4: Angles and Parallel Lines 78
3 6,4 5
2 7,1 8
12
34
56
78

79. Example:If line ABis parallel to line CDand sis parallel to t, find
the measure of all the angles when m< 1 = 100°. Justify your answers.
Lesson 2-4: Angles and Parallel Lines 79
m<2=80°m<3=100°m<4=80°
m<5=100°m<6=80°m<7=100°m<8=80°
m<9=100°m<10=80°m<11=100°m<12=80°
m<13=100°m<14=80°m<15=100°m<16=80°
t
1615
1413
1211
109
87
65
34
21
s
DC
BA

80. Proving Lines Parallel
•If two lines are cut by a transversal and alternate
interiorangles are congruent, then the lines are parallel.DC
BA

81. Ways to Prove Two Lines Parallel
•Show that corresponding angles are equal.
•Show that alternative interior angles are equal.
•In a plane, show that the lines are perpendicular to the
same line.

82. Homework
Pg 305 #6-14e, 18-32e (just answers)
Pg 309 #6-24e (just answers)