© t madas. p a r a l l e l l i n e s n e v e r m e e t what are parallel lines? parallel lines stay...
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© T Madas
© T Madas
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
© T Madas
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
© T Madas
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
© T Madas
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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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
© 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 =
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
© T Madas
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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