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2. Dear Lord,
We thank you a hundredfold for the
love and care that you have given us.
May we return to you, your good
works by multiplying it with love and
respect, adding more faith,
subtracting the unworldly behavior
and evil works and dividing your
given talents to others so we can
sum it all and be united as one,
in your family. In this we pray, Amen.

3. WARM-UP ACTIVITY
Find the measure of the
missing angle without
using a protractor.

4. 48°?

5. 48°48°

6. 155° ?

7. 155° 25°

8. 30°
?

9. 30°
60°

10. 50°
?

11. 40°
50°

12. 28°
?

13. 28°
152°

15. P ____ ____ ____

16. P A I R

17. I ___ ___ ___ R ___ ___ R

18. I N T E R I O R

19. P ___ ___ ___ ___ ___ ___ ___

20. P A R A L L E L

21. V ___ ___ ___ ___ ___ ___ L

22. V E R T I C A L

23. T ___ ___ ___ ___ V ___ ___ ___ ___ L

24. T R A N S V E R S A L

25. A
A ___ ___ ___ ___

26. A N G L E

27. E X ___ ___ ___ ___ ___ R

28. E X T E R I O R

29. PROPERTIES OF
PARALLEL
LINES CUT BY A
TRANSVERSAL

30. Parallel lines are
coplanar lines that never
intersect.

31. Transversal is a line that
intersects two or more lines at
different points.

32. 3
1 2
4
6
57
8
“ Lines and Angles”

33. Postulate
If two parallel lines are cut
by a transversal then the
corresponding angles are
congruent.

34. Given : a II b
transversal t cuts lines a and b
Prove :
Statement
 1. a II b
2. <1 = <2
3.
4.
Reason
 1. Given
 2.
 3.
 4. Transitive Property
a
b
t
12
34

35. Theorem
If two parallel lines
are cut by transversal ,
then alternate interior
angles are congruent.

37. Theorem
If two parallel lines are
cut by transversal ,
then alternate exterior
angles are congruent.

39. Given : a II b
transversal t cuts lines a and b
Prove : are supplementary.
t
a
b
1
2
3
4
Statement Reason
1. a II b
2.
3.
4.
5.
6.
7.
1. Given
2. Linear Pair Postulate
3.
4.
5.
6.
7. Definition of
Supplementary Angles

40. Theorem
 If two parallel lines are cut
by a transversal, then the
interior angles on the same
side of the transversal are
supplementary.

42. Theorem
If two parallel lines are
cut by a transversal,
then the exterior
angles on the same
side of the transversal
are supplementary.

44. Determine whether the following
pairs of angles are congruent or
supplementary.

49. Illustrative Examples
 Given :s II t, m 1 = 5x + 9 and
 m 2 = 3x +11. Find x and the m 1
and m 2.
1 2

50. Given : a II b, m 1 = 4x-7 and
m 2 = 2x +19. Find x and the m 1 and
m 2.
a
b
t
1
2

51. GROUP ACTIVITY

52. 1.In the given figure, find the measure
of the numbered angles if m 1 = 120°
1
4
3 2
5
6
7
8

53. In the given figure find the measure of
the numbered angles if m 1 = 120°
120°
60°
60° 120°
120°
120°
60°
60°

54. 2.Solve for x given that a II b, then find the
measure of angle 1 and 8 if m 1= 2x+25
and m 8 = x + 75.
5 6
7 8
1 2
3 4

55. Answer
x = 50
measure of angle 1=125°
measure of angle 8 = 125°

56. 2x + 4
l1
l2
110°
If || , find x.1 2l l

57. Answer
x = 53

58. Solve for x given that a II b, then find the
measure of angle 6 and 1 if m 6= 4x+ 10
and m 1 = 6x +10.
5 6
7 8
1 2
3 4

59. Solve for x given that a II b, then find the
measure of angle 6 and 1 if m 6= 4x+ 10
and m 1 = 6x +10.
5 74°
7 8
106° 2
3 4
x = 16

60. QUIZ

61.  I. Directions: Identify the following
pairs of whether congruent or
supplementary.
 1. 8 and 6
 2. 2 and 7
 3. 4 and 8 7
 4. 3 and 5 8
 5. 1 and 8
5
6
3
1
4
2

62. 1. Find the measure of the numbered
angles if a II b and the measure of one
angle is given. 2
3
47°
II.

63. 2. Find the value of x for which a II b.
4x°
108°

64. 3. Find the value of x for which a II b.
50°
(3x + 10)°

65. 4.Solve for x given that a II b, then find the
measure of angle 7 and 4 if m 7= 2x -15
and m 4 = x + 17.
5 6
7 8
1 4
3 2

66. ANSWER
 II.1. 2 = 133°, 3= 133°

 2. X = 27
 3. X= 40
 4. X = 32, 7 = 49°, 4 = 49°

67. ASSIGNMENT
Study the problem situation in
Activity 6 on page 453
( Learner's Material ), then
answer the given questions
using the sketch.

68. LIFE is a math equation.
In order to gain the most,
you have to know how to
convert negatives into
positives.
- Anonymous-

69. Geometry
Opportunity is
missed by most
people because it is
dressed in overalls
and looks like work.
Thomas Edis
Today:
•Homework Check
•3.2 Check Up
•Practice

70. Yesterday
Assignment:
• 3.1-3.2 p. 197 #1-14
Opportunity is
missed by most
people because it is
dressed in overalls
and looks like work.
Thomas Edison

71. Identify the vocabulary term for each pair
of angles represented in the picture.
1. ∠3 and ∠6
2. ∠1 and ∠8
3. ∠2 and ∠6
4. ∠1 and ∠6
5. ∠3 and ∠5
3.2 Check Up

72. You named angle pairs formed by parallel lines
and transversals.
• Use theorems to determine the relationships
between specific pairs of angles.
• Use algebra to find angle measurements.

73. Content Standards
G.CO.1 Know precise definitions of angle, circle,
perpendicular line, parallel line, and line segment,
based on the undefined notions of point, line, distance
along a line, and distance around a circular arc.
G.CO.9 Prove theorems about lines and angles.
Mathematical Practices
1 Make sense of problems and persevere in solving
them.
3 Construct viable arguments and critique the
reasoning of others.

74. 3.2 Angles and Parallel Lines
Objectives:
1. Properties of parallel lines and
transversals
2. Using properties of parallel lines
in proofs
Vocabulary:
parallel, transversal, corresponding,
alternate interior, alternate exterior,
consecutive interior

75. If 2 parallel lines are cut by a transversal, then:
corresponding angles are congruent.
alternate interior angles are congruent.
alternate exterio
corresponding angles
alternate interior angles
alternate ex
1 2
4 3
5 6
8 7
3.2 Angles and Parallel Lines

76. 2x + 4
l1
l2
110°
If || , find x.1 2l l

77. If || , find x and y.1 2l l
y + 20
l1
l2
°75
x
x = 105
y = 85

79. Given: ||
||
Prove: 1 2
1
3
l l
l l
2
4
∠ ≅ ∠ 1
3
2
Statements Reasons
1. Given  ALWAYS
4. Transitive Property of
Congruency.

80. Geometry
Assignment:
• 3.2 p. 183 #5, 8, 25, 49
Opportunity is
missed by most
people because it is
dressed in overalls
and looks like work.
Thomas Edison