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Para

llel l

ines

nev

er

mee

t

What are parallel lines?

Parallel lines stay the same distance apart

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What are perpendicular lines?

Perpendicular lines are lines at right angles with each other

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Transversal

1 234

6578

Vertically Opposite Angles

Vertically Opposite Angles are EQUAL

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Transversal

1 234

65

78

Corresponding Angles

Corresponding Angles are EQUAL

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Transversal

1 234

65

78

Alternate Angles or Z-angles

Alternate Angles are EQUAL

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Recognisingthese

Special Angles

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Which angle is vertically opposite to angle a ?

Which is the corresponding angle to angle a ?

a12 3

4 56 7

Which angle is vertically opposite to angle k ?

Which is the corresponding angle to angle k ?

k5

7

24

1

6

3

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Which is the corresponding angle to angle n ?

Which angle is alternate angle to angle n ?

n1

6

32

547

Which angle is vertically opposite to angle p ?

Which is the alternate angle to angle p ?

p

54

2

7

1

6

3

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t

12

3

4

5

6

7

Which angle is vertically opposite to angle t ?

Which is the corresponding angle to angle t ?

Which is the corresponding angle to angle q ?

Which angle is alternate angle to angle q ?

q2

7

31

4 56

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b1

23

45

67

Which angle is vertically opposite to angle b ?

Which is the corresponding angle to angle b ?

Which is the corresponding angle to angle h ?

Which angle is alternate angle to angle h ?

h

6

1

5

7

43

2

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Which angle is alternate angle to angle x ?

Which are the corresponding angles to angle x ?

x

13

2

8 9

10 11

4 5

7

1213

1415

6

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Which angle is alternate angle to angle x ?

Which are the corresponding angles to angle x ?

x

13

2

8 9

10 11

4 5

6 7

1213

1415

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Which angle is alternate angle to angle x ?

Which are the corresponding angles to angle x ?

x

13

2

8 9

10 11

4 5

6 7

1213

1415

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Which angle is alternate angle to angle x ?

Which are the corresponding angles to angle x ?

x

13

2

8 9

10 11

4 5

6 7

1213

1415

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Some Practice

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70°

?

50°

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?

One of the many solutions:

70° 50°

70°

50°70°

60°

60°

70° 50°

Vertically OppositeVertically Opposite

Alternate anglesCorresponding angles

Vertically OppositeAngles in a triangle

Vertically opposite

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One of the many solutions:

70° 50°

70° 50°

How can we find thisangle in one quickStep from this position?

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One of the many solutions:

70° 50°

70° 50°

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More Practice

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62°

118°

62°

62°

straight line

corresponding

vertically opposite

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straight line

62°

118°118°

corresponding

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48°

56°

48°

48°

48°

56°

vertically opposite

alternate

OR

corresponding

corresponding

corresponding

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41°

54°

54°41°

alternate

corresponding

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46°

47°

134°

47°

134°

alternate

straight line

corresponding

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52°

52°

38°

38°

vertically opposite

angles in a triangle

alternate

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© T Madas

2x

3x

2x

Find the value of x and hence calculate these two angles

Alternate Angles

Straight Line

3x + 2x = 180°

5x = 180°

x = 36°

72°

108°

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100°

Find the value of the angle marked in purple

52°

48°

52°

48°

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Find the value of the angle marked in purple

27°

58°

27°

58°

275°

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Find the value of the angle marked in purple

125°

105°

75°

75° 55°

50°

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Find the value of x and hence calculate these two angles

2x

3x2x

3x + 2x = 90°

5x = 90°

x = 18°

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Find the value of x and hence calculate these two angles

3x + 2x = 90°

5x = 90°

x = 18°

36°

54°

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Find the value of angle x ONLY

x

aa

b b2a

2a + 2b = 180°

a + b = 90°

90°

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© T Madas

A farm gate consists of three parallel planks of wood with a metal bar running diagonally for extra support, as shown in the diagram.

Calculate the angles x, y and z.

30°

y

x

z

x and the 30° angle are ALTERNATE ANGLES

x = 30°

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A farm gate consists of three parallel planks of wood with a metal bar running diagonally for extra support, as shown in the diagram.

Calculate the angles x, y and z.

30°

y

x

z x =

y =

30°

30°

y and the 30° angle are CORRESPONDING ANGLES

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A farm gate consists of three parallel planks of wood with a metal bar running diagonally for extra support, as shown in the diagram.

Calculate the angles x, y and z.

30°

y

x

z x =

y =

z =

30°

30°

150°

ALTERNATE ANGLES

30°

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© T Madas

A B

CD E

25°

55°

ABCD is a trapeziumADB = 90°DBE = 25° and EBC = 55°

1. Calculate ABD2. Calculate DAB3. Calculate BDC

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A

CD E

25°

55°

ABCD is a trapeziumADB = 90°DBE = 25° and EBC = 55°

1. Calculate ABD2. Calculate DAB3. Calculate BDC

B30°

30°

60°

60°

Alternate Angles

Angles of a triangle

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A

CD E

25°

55°

ABCD is a trapeziumADB = 90°DBE = 25° and EBC = 55°

1. Calculate ABD2. Calculate DAB3. Calculate BDC

B30°

30°

60°

60°

30°

30°

Alternate Angles

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