Chapter 9 PARALLEL LINES SMPK PENABUR GADING SERPONG

Lines A. Position of line

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1 Horizontal line

2 Vertical line 3 Curve line

Lines B. Position of two lines

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1 Intersection lines : two lines that joining in a point


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2 Perpendicular lines : two lines that joining in a point and form 90 degree angle


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3Skew lines : two lines that not intersects and not parallel


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4 Coincide lines : two lines that overlap ( match ) each other

a

b


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4 Parallel lines : two lines not intersects and always have the same distance

a

b

Chapter 3

Parallel Lines

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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

Parallel lines in our daily life

Parallel Lines

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Parallel Lines


SMPK Penabur GS

Parallel Lines

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Parallel lin

es in o

ur

daily life

Parallel Lines

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PARALLEL LINES•Def: line that do not intersect and always

have the same distance.

•Illustration:

•Notation: l || m AB || CD

lm

A

B

C

D

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TransversalDefinition: 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.

transversalm

n

1 23 4

5 67 8

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16

INTERIOREXTERIOR

EXTERIOR

m

l

k

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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Angles and Parallel LinesWhen a transversal intersects parallel lines, eight anglesare formed.

transversal1 2

3 4

5 67 8

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Vertical Angles & Linear PairVertical Angles:

Linear Pair:

1 4, 2 3, 5 8, 6 7

Two angles that are opposite angles. Vertical angles are congruent.

1 & 2 , 2 & 4 , 4 &3, 3 & 1, 5 & 6, 6 & 8, 8 & 7, 7 & 5

Supplementary angles that form a line (sum = 180)

1 23 4

5 67 8

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Corresponding Angles

Two angles that occupy corresponding positions.

Top Left

t

Top Left

Top Right

Top Right

Bottom Right

Bottom Right

Bottom Left

Bottom Left

Ð1 5Ð2 6Ð3 7Ð4 8

1 2

3 4

5 6

7 8

SMPK Penabur GS


If two parallel lines cut by transversal, so the magnitude of corresponding angles are equal t

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Find the measures of the missing angles

145

?

t

35

145


SMPK Penabur GS

Alternate Interior AnglesTwo angles that lie between parallel lines on

opposite sides of the transversal

t

Ð3 6Ð4 5

1 2

3 4

5 6

7 8

SMPK Penabur GS

If two parallel lines cut by transversal, so the magnitude of alternate interior angles are equal t

SMPK Penabur GS

Alternate Interior Angles


82

?

t

98 82


SMPK Penabur GS

Two angles that lie outside parallel lines on opposite sides of the transversal

t

Ð2 7Ð1 8

1 2

3 4

5 6

7 8

Alternate Exterior Angles

SMPK Penabur GS

If two parallel lines cut by transversal, so the magnitude of alternate exterior angles are equal t

SMPK Penabur GS


Alternate Exterior AnglesFind the measures of the missing angles

120

?

t

60 120

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Consecutive ( Allied ) Interior Angles

Two angles that lie between parallel lines on the same sides of the transversal

t

Ð3 +5 = 1800

Ð4 +6 = 1800

1 2

3 4

5 6

7 8

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If two parallel lines cut by transversal, then alternate interior angles are supplementaryt

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Consecutive (Allied) Interior Angles

+ =1800

Consecutive ( Allied ) Interior Angles


?

t

135

45

1800 – 1350 = 450

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Two angles that lie outside parallel lines on the same sides of the transversal.

t

Ð1 + 7 = 1800

Ð2 + 8 = 1800

1 2

3 4

5 6

7 8

Consecutive Exterior Angles

SMPK Penabur GS

If two parallel lines cut by transversal, then alternate exterior angles are supplementaryt

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Consecutive (Allied) Exterior Angles

+= 1800

Consecutive Exterior Angles


?

t

117

63

1800 – 1170 = 630

Exercise Find the value of angles number 1 to 7 !

5701

2 3

4 5

6 7

1 = 1800 – 570 = 1230

2 = 570

3 = 1230

4 = 1230

5 = 570

6 = 570

7 = 1230

Parallel Lines

Part II: Equations

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• Name the angle relationship• Are they congruent or supplementary?• Find the value of x

125

t

5x

5x = 125

5 5x = 25

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2x + 1

t

151

2x = 150

2 2x = 75

2x + 1 = 151- 1 - 1

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Consecutive Interior Angles


81

t

7x + 15

supp

7x = 847 7x = 12

7x + 96 = 180 - 96 - 96

7x + 15 + 81 = 180

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3x

t

2x + 20

20 = x

2x + 20 = 3x- 2x - 2x

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7X + 30 = 15X -18- 30 -30

7X = 15X - 48-15X -15X

-8X= - 48-8 -8

X = 6

Find the value for X:

Both angles are ALTERNATE EXTERIOR and the lines are parallel, so the angles are equal

7X + 30

15X - 18

14X + 6 = 8X + 54- 6

-614X = 8X + 48-8X -8X6X = 486 6X = 8


Both angles are ALTERNATE INTERIOR and the lines are parallel, so the angles are equal

8X + 54

14X + 6

16X + 9 = 9X + 58- 9

-916X = 9X + 49-9X -9X7X = 497 7X = 7


Both angles are CORRESPONDING and the lines are parallel, so the angles are equal

9X + 5816X +

9


3X + 17

17X + 23

Both angles are CONSECUTIVE INTERIOR ANGLES, so they are SUPPLEMENTARY:

(3X + 17) + (17X + 23) = 180

3X + 17X + 17 + 23 = 180

20X + 40 = 180 -40 -

4020X = 14020 20

X = 7

Both angles are ALTERNATE EXTERIOR :

8X + 26 = 12X -14 - 26 -

268X = 12X - 40-12X -

12X-4X= - 40-4 -4X = 10

=12( ) -14

10= 120 -

14= 106°

Angles form a LINEAR PAIR:

Z + 106° = 180° -106 -106Z = 74

8X + 26

12X – 14

Z

Find the value for X and Z:

Both angles are ALTERNATE INTERIOR :

5Z + 13 = 93 – 3Z - 13 -13

5Z = -3Z + 80+ 3Z + 3Z

8Z = 808 8

Z = 10

= 93 – 3( )

10= 93 - 30= 63°

Y + 63° = 90°-63 -63

Y = 27°

These are complementary:

5Z + 13

93 – 3Z

Y

Find the value for Y and Z in the figure below:

Both angles are ALTERNATE INTERIOR :

6Y + 15 = 75 – 14Y- 15 -15

6Y = -14Y +60+ 14Y +

14Y20Y = 6020 20Y = 3

= 6( ) + 15

3= 18 + 15= 33°

X + 33° = 90°-33 -33

X = 57°

These are complementary:

6Y + 15

75 – 14Y

X

Find the value for X and Y in the figure below:

35° 58°

87°

+ +

C

Cm

B

Bm

A

Am =180°35° + 87° + 58° =

180°The sum of the interior angles of a triangle is always 180°

ANGLE SUM THEOREM:

48

103°77

°

77°

65° 1. Vertical

Angles2. Linear pair:

180°-103° = 77°180°-65°= 115°

115°

115°

3. Corresponding Angles

65°

65°115

°115°

4. Vertical Angles

5. Linear Pair:180°-65°=

115°6. Interior Angle Sum in triangle is 180°:

180°-77°-65° = 38°

38°

7. Vertical Angles

38°


38°

38°

9. Linear Pair180°-38°= 142°

142° 142

°142°

142°

103°

65°

Find all the unknown angles in the figure below:

110°70

°

70°

85° 1. Vertical

Angles2. Linear pair:

180°-110° = 70°180°-85°= 95°

95°95°


85°

85°95° 95°

4. Vertical Angles

5. Linear Pair:180°-85°=

95°6. Interior Angle Sum in triangle is 180°:

180°-70°-85° = 25°

25°

7. Vertical Angles

25°


25°

25°

9. Linear Pair180°-25°= 155°

155° 155

°155°

155°

110°

85°

Find all the unknown angles in the figure below:

Alternate Exterior Angles:Z =

145°

2X + 5

5Y + 5

Z

145°

Find the value for X, Y and Z in the figure below:


145°Linear Pair and supplementary:

145° + (5Y + 5)° = 180° 150 + 5Y =

180-150 -150

5Y = 305 5

Y = 6

2X + 5

5Y + 5

Z

145°




145° + (5Y + 5)° = 180° 150 + 5Y =

180-150 -150

5Y = 305 5

Y = 6Corresponding angles:2X + 5 = 145°-5 -

52X = 1402 2X = 70

2X + 5

5Y + 5

Z

145°


Alternate Exterior Angles:T =

140°

2R – 15

4S – 20

T

140°

Find the value for R, S and T in the figure below:

Alternate Exterior Angles:T =


140° + (4S – 20 )° = 180° 120 + 4S =

180-120 -120

4S = 604 4

S = 15

2R – 15

4S – 20

T

140°




140° + (4S – 20 )° = 180°

120 + 4S = 180-120 -

1204S = 604 4

S = 15

Corresponding angles:2R – 15 = 140°+15

+152R = 1552 2R = 77.5

2R – 15

4S – 20

T

140°


Thank you for your

attentionGod Bless You ☺

Chapter 9 PARALLEL LINES SMPK PENABUR GADING SERPONG

Technology

Transcript of Chapter 9 PARALLEL LINES SMPK PENABUR GADING SERPONG