pairs of angles
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Pairs of Angles : Types• Adjacent angles
• Vertically opposite angles
• Complementary angles
• Supplementary angles
• Linear pairs of anglesNM Spirit
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Adjacent AnglesTwo angles that have a common vertex and a common ray are called adjacent angles.
C
D
B
A
Common ray
Common vertex
Adjacent Angles ABD and DBC
Adjacent angles do not overlap each other.
D
EF
A
B
C
ABC and DEF are not adjacent angles
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Vertically Opposite AnglesVertically opposite angles are pairs of angles formed by two lines intersecting at a point.
ÐAPC = ÐBPD
ÐAPB = ÐCPD
A
DB
C
P
Four angles are formed at the point of intersection.
Point of intersection ‘P’ is the common vertex of the four angles.
Vertically opposite angles are congruent.
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If the sum of two angles is 900, then they are called complementary angles.
600
A
BC
300
D
EF
ÐABC and ÐDEF are complementary because
600 + 300 = 900
ÐABC + ÐDEF
Complementary Angles
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If the sum of two angles is 1800 then they are called supplementary angles.
ÐPQR and ÐABC are supplementary, because
1000 + 800 = 1800
RQ
PA
BC
1000 800
ÐPQR + ÐABC
Supplementary Angles
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Two adjacent supplementary angles are called linear pair of angles.
A
600 1200
PC D
600 + 1200 = 1800
ÐAPC + ÐAPD
Linear Pair Of Angles
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A line that intersects two or more lines at different points is
called a transversal.
Line L (transversal)
BALine M
Line NDC
P
Q
G
F
Pairs Of Angles Formed by a Transversal
Line M and line N are parallel lines.
Line L intersects line M and line N at point
P and Q.
Four angles are formed at point P and another four at point
Q by the transversal L.
Eight angles are formed in all by
the transversal L.
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Pairs Of Angles Formed by a Transversal
• Corresponding angles
• Alternate angles
• Interior angles
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Corresponding AnglesWhen two parallel lines are cut by a transversal, pairs of corresponding angles are formed.
Four pairs of corresponding angles are formed.
Corresponding pairs of angles are congruent.
ÐGPB = ÐPQE
ÐGPA = ÐPQD
ÐBPQ = ÐEQF
ÐAPQ = ÐDQF
Line MBA
Line ND E
L
P
Q
G
F
Line L
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Alternate AnglesAlternate angles are formed on opposite sides of the transversal and at different intersecting points.
Line MBA
Line ND E
L
P
Q
G
F
Line L
ÐBPQ = ÐDQP
ÐAPQ = ÐEQP
Pairs of alternate angles are congruent.
Two pairs of alternate angles are formed.
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The angles that lie in the area between the two parallel lines that are cut by a transversal, are called interior angles.
A pair of interior angles lie on the same side of the transversal.
The measures of interior angles in each pair add up to 1800.
Interior Angles
Line MBA
Line ND E
L
P
Q
G
F
Line L
6001200
1200600
ÐBPQ + ÐEQP = 1800
ÐAPQ + ÐDQP = 1800
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