1. Agenda for today: ACT Warm up Return tests Start section 3.1
Welcome back!
Agenda for today:
ACT Warm up
Return tests
Start section 3.1

2. Lesson 3-1 Learning Targets
I can identify the relationships between lines and planes
I can name angles formed by parallel lines and transversals 2

3. lines that are coplanar and don’t intersect
lines that are not coplanar and don’t intersect
planes that don’t intersect

4. 6
plane DCG
plane DAE

5. BC AD CG

6. AE AD BF BC EF DC HG EH DH FG CG

7. a line that intersects two or more lines in a plane
transversal

8. ∠3, ∠4,
∠5, ∠6
∠1, ∠2,
∠7, ∠8

9. ∠4 and ∠5
∠3 and ∠6
∠1 and ∠8
∠2 and ∠7

10. ∠4 and ∠6
∠3 and ∠5
∠1 and ∠7
∠2 and ∠8
∠1 and ∠5
∠2 and ∠6
∠3 and ∠7
∠4 and ∠8

11. Warm Up Name all the lines parallel to AD. (2)
Name the plane parallel to ADC. (1)
Name the lines that intersects with AD. (4)
Name the planes that intersects with ADC. (4)
Name a line skew to AD.
Name a line skew to AB

12. AIA
AEA CA
CIA
CIA
AEA
AIA
CIA CA CA
AEA
AIA CA

13. AIA CA
AEA
CIA
AEA
AIA CA

14. FG CD CB GH GF DH BF AE AB EF AD EH

15. ASSIGNMENT:
3.1 Worksheet

16. Lesson 3-2 Learning Targets
I can use properties of parallel lines to find angle measures.
I can use properties of parallel lines to determine congruent angles 16

17. l m
l ∥ m

18. congruent
∠1 ≅ ∠5
∠2 ≅ ∠6
∠3 ≅ ∠7
∠4 ≅ ∠8

19. congruent
∠3 ≅ ∠6
∠4 ≅ ∠5

20. congruent
∠1 ≅ ∠8
∠2 ≅ ∠7

21. supplementary
m∠3 + m∠5 = 180
m∠4 + m∠6 = 180

22. 125°
55°
55°
125°
55°
55°
125°
125°
125°
55°
55°
55°
125°

23. 92°
106°
92°
74°
92°
106°
88°
74°
106°

24. 78°
102°
78°
102°
78°
78°
102°
102°

25. 2x – 10
= x + 15
x – 10 = 15
x = 25
= 40°
m∠5 = 2(25) – 10
m∠6 =
= 40°

26. 9x + 12
= 42
9x = 30
x = 3 1/3
= 42°
m∠1 = 9(3 1/3 ) + 12

27. 46
8x – 6
+ 6x + 46
= 180
14x + 40 = 180
106°
14x = 140
x = 10
= 106°
m∠4 = 6(10) +46

28. 46
9y – 5
+ 106
= 180
9y = 180
106°
9y = 79
y = 8.78
x = 10, y = 8.78

29. 114°
9a + 6
= 10a – 6
6 = a – 6
12 = a
= 114°
m∠2 = 10(12) – 6

30. 114°
5b + 14
= 114
5b = 100
b = 20
a = 12, b = 20

31. 80°
100°
80°
68°
80°
68°
100°
112°

32. 8x – 10
= 7x
70°
x = 10
6y + 20
+ 70
= 180
6y + 90 = 180
6y = 90
y = 15

33. Warm Up

35. Learning Target Check! Section 3.1
I can identify the relationships between lines and planes
I can name angles formed by parallel lines and transversals
Section 3.2
I can use properties of parallel lines to find angle measures.
I can use properties of parallel lines to determine congruent angles

36. Lesson 3-3 Learning targets
I can find slopes of lines
I can use slope to determine if lines are parallel or perpendicular 36

37. rise
run
run
rise
m =
y2 – y1
x2 – x1

38. m =
y2 – y1
x2 – x1
m =
2 – -2
-1 – -3
m =
2 + 2
-1 + 3
m = 4 2
= 2

39. m =
y2 – y1
x2 – x1
m =
0 – -1
-4 – 0
m =
0 + 1
-4 – 0
m = 1 -4
= – 1 4

40. m =
y2 – y1
x2 – x1
m =
5 – 5
-3 – 1
m = -4
= 0
Horizontal lines always have slope = 0!

41. m = y2 – y1 x2 – x1 m = -4 – 3 6 – 6 m = -7 = undefined
= undefined
Vertical lines always have undefined slope!

42. Have equal slopes
m = 3/4
m = 3/4

43. Have opposite, reciprocal slopes
m = -4/3
m = 3/4

44. perpendicular
Slope of AB:
Slope of CD:
m =
7 – -5
4 – -2
m =
-2 – 2
8 – 0
m = 12 6
m = -4 8
= – 1 2
= 2

45. neither
parallel
neither
perpendicular

46. Warm Up

48. Lesson 3-4 Learning targets
I can construct perpendicular lines through a point.
I can construct parallel lines through a point. 48

49. Review!

50. Constructions
Complete the remaining constructions using the directions on your table. Follow the steps carefully!

51. ASSIGNMENT:
Worksheet!

54. Learning Target Check! Section 3.3 I can find slopes of lines.
I can use slope to identify parallel lines.
I can use slope to identify perpendicular lines.
Section 3.4
I can construct parallel and perpendicular lines.

55. Lesson 3-5 learning targets
I can prove that lines are parallel based on given angle relationships
I can prove that angles are congruent or supplementary based on parallel lines. 55

56. congruent
parallel
CA ≅ → || lines

57. congruent
parallel
AIA ≅ → || lines

58. congruent
parallel
AEA ≅ → || lines

59. CIA supplementary → || lines
parallel
CIA supplementary → || lines

60. AIA ≅ → || lines

61. CA ≅ → || lines

62. CIA supplementary → || lines

63. AEA ≅ → || lines

65. AIA ≅ → || lines

69. Given
Given
Transitive
AIA ≅ → || lines

70. ASSIGNMENT:
3.5 Worksheet

71. Your golden foldable from yesterday
Warm Up Activity…
Have out…
Your golden foldable from yesterday
The stack of angle pair cards on your tables.
Directions: When I show a diagram, hold up the card with the correct angle pairing. Use your foldable if you are unsure!

72. 2 1 4 3 5 6 7 8

73. 1 2 4 3 6 5 8 7

74. 1 2 4 3 5 6 8 7

75. 1 2 3 4 6 5 8 7

76. 2 10

77. 6 16

78. 10 4

79. 7 16

80. BONUS… A little tricky…10 8

81. 0. l ∥ m
0. Given
1. ∠10 ≅ ∠16
1. || lines → AEA ≅

82. 0. ∠2 ≅ ∠12
0. Given
1. r ∥ s
1. AIA ≅ → || lines

83. 0. l ∥ m
0. Given
1. m∠3 + m∠6 = 180
1. || lines → CIA supp

84. 0. ∠7 ≅ ∠15
0. Given
1. r ∥ s
1. CA ≅ → || lines

85. 0. p ∥ q
0. Given
1. m ∥ n
1. Given
2. || lines → CA ≅
2. ∠4 ≅ ∠6
3. ∠6 ≅ ∠5
3. || lines → CA ≅
4. Transitive
4. ∠4 ≅ ∠5

88. 1. Name a pair of Alternate Interior Angles (AIA).
B. ∠8 , ∠14
C. ∠6 , ∠16
D. ∠7 , ∠14
2. Name a pair of Corresponding Angles (CA)
F. ∠3 , ∠4
G. ∠3 , ∠9
H. ∠3 , ∠13
J. ∠3 , ∠7
3. Name a pair of Consecutive Interior Angles (CIA).
A. ∠7 , ∠14
B. ∠3 , ∠11
C. ∠2 , ∠12
D. ∠7 , ∠8

89. Explain how you would find the measures of the numbered angles in this figure. Use complete sentences.
115°
65° 4
65° 2
115° 3