This document discusses parallel lines and their properties. It defines parallel lines as lines that do not intersect and always have the same distance between them. It then covers different types of angles formed when parallel lines are intersected by a transversal line, including corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles, and consecutive exterior angles. It states properties of these angles, such as corresponding angles being congruent and alternate interior angles and exterior angles being congruent. Examples are given of finding missing angle measures using these properties.

1. SMPK PENABUR GS
Lines
A. Position of line
1 Horizontal line
2 Vertical line 3 Curve line

2. SMPK PENABUR GS
Lines
B. Position of two lines
1 Intersection lines : two lines that joining in a point

3. SMPK PENABUR GS
Lines
B. Position of two lines
Perpendicular lines : two lines that joining in a point
2
and form 90 degree angle

4. SMPK PENABUR GS
Lines
B. Position of two lines
3 Skew lines : two lines that not intersects and not parallel

5. SMPK PENABUR GS
Lines
B. Position of two lines
4 Coincide lines : two lines that overlap ( match ) each other
a
b

6. SMPK PENABUR GS
Lines
B. Position of two lines
4 Parallel lines : two lines not intersects and always have
the same distance
a
b

7. SMPK PENABUR GS
Chapter 3
Parallel Lines

8. Vocabulary
• Parallel Lines = garis sejajar
• Skew lines = garis berpotongan dan tidak sejajar
• Transversal lines = garis yang memotong dua garis
dititik yang berbeda
• Interior angles = sudut dalam
• Exterior angles = sudut luar
• Corresponding angles = sudut sehadap
• Alternate interior angles = sudut dalam berseberangan
• Alternate exterior angles = sudut luar berseberangan
• Consecutive interior angles = sudut dalam sepihak
• Consecutive exterior angles = sudut luar sepihak
• Vertical angles = sudut bertolak –belakang

9. Parallel Lines
Parallel lines in our daily life
SMPK Penabur GS

10. Parallel Lines
Parallel lines in our daily life
SMPK Penabur GS

11. Parallel Lines
Parallel lines in our daily life
SMPK Penabur GS

12. Parallel Lines
Parallel lines in our daily life
SMPK Penabur GS

13. Parallel Lines
SMPK Penabur GS

14. PARALLEL LINES
• Def: line that do not intersect and always have
the same distance.
B
• Illustration:
A D
l
m C
• Notation: l || m AB || CD
SMPK Penabur GS

15. Transversal
Definition: A line that intersects two or more lines in a
plane at different points is called a transversal.
When a transversal t intersects line n and m, eight angles
are formed.
transversal
m 1 2
3 4
5 6
n 7 8
SMPK Penabur GS

16. k m
l
EXTERIOR
16
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

17. Angles and Parallel Lines
When a transversal intersects parallel lines, eight angles
are formed.
transvers
1 al
2
3 4
5 6
7 8
SMPK Penabur GS

18. Vertical Angles & Linear
Pair
Vertical Angles: Two angles that are opposite angles.
Vertical angles are congruent.
 1   4,  2   3,  5   8,  6   7
Linear Pair: Supplementary angles that form a line (sum =
180)
1 & 2 , 2 & 4 , 4 &3, 3 & 1,
5 & 6, 6 & 8, 8 & 7, 7 & 5
12
3 4
56
7 8 SMPK Penabur GS

19. Corresponding Angles
 Two angles that occupy corresponding positions.
t
Top Left Top Right 1   5
2   6
1 2
3 4
3   7
Bottom Left Bottom Right
Top Left 5 6 Top Right 4   8
7 8
Bottom Left Bottom Right
SMPK Penabur GS

20. Corresponding Angles
If two parallel lines cut by transversal, so the
magnitude of corresponding angles are equal
t
SMPK Penabur GS

21. Corresponding Angles
 Find the measures of the missing angles
t
145  35 
145  ?
SMPK Penabur GS

22. Alternate Interior Angles
 Two angles that lie between parallel lines on
opposite sides of the transversal
t
3   6
1 2
3 4
4   5
5 6
7 8
SMPK Penabur GS

23. Alternate Interior Angles
If two parallel lines cut by transversal, so the
magnitude of alternate interior angles are equal
t
SMPK Penabur GS

24. Alternate Interior Angles
 Find the measures of the missing angles
t
82 
98  ? 82 
SMPK Penabur GS

25. Alternate Exterior Angles
 Two angles that lie outside parallel lines on opposite
sides of the transversal
t
2   7
1 2
3 4
1   8
5 6
7 8
SMPK Penabur GS

26. Alternate Exterior Angles
If two parallel lines cut by transversal, so the
magnitude of alternate exterior angles are equal
t
SMPK Penabur GS

27. Alternate Exterior Angles
 Find the measures of the missing angles
t
120 
60  ? 
120
SMPK Penabur GS

28. Consecutive ( Allied ) Interior Angles
 Two angles that lie between parallel lines on the
same sides of the transversal
t
3 +5 = 1800
1 2
3 4
4 +6 = 1800
5 6
7 8
SMPK Penabur GS

29. Consecutive (Allied) Interior Angles
If two parallel lines cut by transversal, then alternate
interior angles are supplementary
t
+ = 1800
SMPK Penabur GS

30. Consecutive ( Allied ) Interior Angles
 Find the measures of the missing angles
t
1800 – 1350 = 450
135 
? 45 
SMPK Penabur GS

31. Consecutive Exterior Angles
 Two angles that lie outside parallel lines on the same
sides of the transversal.
t
1 +  7 = 1800
1 2
3 4
2 +  8 = 1800
5 6
7 8
SMPK Penabur GS

32. Consecutive (Allied) Exterior Angles
If two parallel lines cut by transversal, then alternate
exterior angles are supplementary
t
+ = 1800
SMPK Penabur GS

33. Consecutive Exterior Angles
 Find the measures of the missing angles
t
117  1800 – 1170 = 630
63  ?

34. Exercise
Find the value of angles number 1 to 7 !
4 5 1 570
6 7 2 3

35. Parallel Lines
Part II: Equations
SMPK Penabur GS

36. Alternate Exterior Angles
• Name the angle relationship
• Are they congruent or supplementary? 
• Find the value of x
t
5x = 125
125 
5 5
x = 25
5x 
SMPK Penabur GS

37. Corresponding Angles
• Name the angle relationship
• Are they congruent or supplementary? 
• Find the value of x
t
2x + 1 = 151
2x + 1 -1 -1
2x = 150
151 2 2
x = 75
SMPK Penabur GS

38. Consecutive Interior Angles
• Name the angle relationship
• Are they congruent or supplementary? supp
• Find the value of x
t
7x + 15 + 81 = 180
7x + 96 = 180
81 - 96 - 96
7x + 15 7x = 84
7 7
x = 12
SMPK Penabur GS

39. Alternate Interior Angles
• Name the angle relationship
• Are they congruent or supplementary? 
• Find the value of x
t
2x + 20 = 3x
3x
- 2x - 2x
2x + 20 20 = x
SMPK Penabur GS

40. Find the value for X:
7X + 30
15X - 18
Both angles are ALTERNATE EXTERIOR and the lines are parallel, so the angles are equal
7X + 30 = 15X -18
- 30 -30
7X = 15X - 48
-15X -15X
-8X= - 48
-8 -8
X=6

41. Find the value for X:
14X + 6
8X + 54
Both angles are ALTERNATE INTERIOR and the lines are parallel, so the angles
are equal
14X + 6 = 8X + 54
-6 -6
14X = 8X + 48
-8X -8X
6X = 48
6 6
X=8

42. Find the value for X:
9X + 58
16X + 9
Both angles are CORRESPONDING and the lines are parallel, so the angles
are equal
16X + 9 = 9X +
58 - 9 -
9
16X = 9X +
49
-9X -9X
7X = 49
7
7
X=7

43. Find the value for X:
Both angles are CONSECUTIVE INTERIOR
3X + 17 ANGLES, so they are SUPPLEMENTARY:
(3X + 17) + (17X + 23) = 180
3X + 17X + 17 + 23 = 180
17X + 23
20X + 40 = 180
-40 -40
20X = 140
20 20
X=7

44. Find the value for X and Z:
8X + 26 Z
12X – =12(1 ) -
14 = 120 - 14
14 0
= 106°
Both angles are ALTERNATE EXTERIOR :
8X + 26 = 12X -14
- 26 -26
8X = 12X - 40 Angles form a LINEAR PAIR:
-12X -12X
Z + 106° = 180°
-4X= - 40 -106 -
-4 - 106
Z = 74
4
X = 10

45. Find the value for Y and Z in the figure below:
5Z + 13
Y These are
complementary:
Y + 63° = 90°
-63 -63
93 – 3Z Y = 27°
= 93 – 3( )
10
= 93 -
=
30
63° Both angles are ALTERNATE INTERIOR :
5Z + 13 = 93 – 3Z
- 13 -13
5Z = -3Z + 80
+ 3Z + 3Z
8Z = 80
8 8
Z = 10

46. Find the value for X and Y in the figure below:
6Y + = 6( 3 ) + 15
X 15 = 18 + 15 These are
= complementary:
X + 33° = 90°
33° -33 -33
75 – X = 57°
14Y
Both angles are ALTERNATE INTERIOR :
6Y + 15 = 75 – 14Y
- 15 -15
6Y = -14Y
+60
+ 14Y + 14Y
20Y = 60
20 20
Y=3

47. ANGLE SUM
THEOREM: B
87°
35° 58°
A C
m A + m B + m C = 180°
35° + 87° + 58° = 180°
The sum of the interior angles of a triangle is always
180°

48. Find all the unknown angles in the figure
below:
65°
1. Vertical Angles
115°
115° 2. Linear pair:
65° 65°
180°-103° = 77°
115° 115°
180°-65°= 115°
103° 65° 3. Corresponding Angles
77° 77°
38° 4. Vertical Angles
103° 142°
142° 38° 5. Linear Pair:
38°
142° 180°-65°= 115°
142°
38° 6. Interior Angle Sum in
triangle is 180°:
180°-77°-65° = 38°
7. Vertical Angles
8. Corresponding Angles
9. Linear Pair
180°-38°= 142° 48

49. Find all the unknown angles in the figure
below:
85°
1. Vertical Angles
95°
95° 2. Linear pair:
85° 85°
180°-110° = 70°
95° 95° 180°-85°= 95°
110° 85° 3. Corresponding Angles
70° 70°
25° 4. Vertical Angles
110° 155°
155° 25° 5. Linear Pair:
25°
155° 180°-85°= 95°
155°
25° 6. Interior Angle Sum in
triangle is 180°:
180°-70°-85° = 25°
7. Vertical Angles
8. Corresponding Angles
9. Linear Pair
180°-25°= 155°

50. Find the value for X, Y and Z in the figure below:
Alternate Exterior Angles:
Z Z = 145°
2X + 5
5Y + 5
145
°

51. Find the value for X, Y and Z in the figure below:
Alternate Exterior Angles:
Z Z = 145°
Linear Pair and supplementary:
2X + 5
145° + (5Y + 5)° =
5Y + 5 180° 150 + 5Y = 180
145 -150 -
° 150
5Y = 30
5 5
Y=6

52. Find the value for X, Y and Z in the figure below:
Alternate Exterior Angles:
Z Z = 145°
Linear Pair and supplementary:
2X + 5
145° + (5Y + 5)° =
5Y + 5 180° 150 + 5Y = 180
145 -150 -
° 150
5Y = 30
5 5
Corresponding angles:
Y=6
2X + 5 = 145°
-5 -5
2X = 140
2 2
X = 70

53. Find the value for R, S and T in the figure below:
Alternate Exterior Angles:
T T = 140°
2R –
15
4S – 20
140
°

54. Find the value for R, S and T in the figure below:
Alternate Exterior Angles:
T T = 140°
Linear Pair and supplementary:
2R –
140° + (4S – 20 )° =
15
4S – 20 180° 120 + 4S = 180
140 -120 -
° 120
4S = 60
4 4
S = 15

55. Find the value for R, S and T in the figure
below:
Alternate Exterior Angles:
T Z = 140°
Linear Pair and supplementary:
2R –
140° + (4S – 20 )° = 180°
15
4S – 20 120 + 4S = 180
140 -120 -
° 120
4S = 60
4 4
Corresponding angles:
S = 15
2R – 15 =
140°+15
+15
2R =
2
155 2
R=
77.5

56. Thank you for
your attention
God Bless You