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Transversal
A line that intersects two or more lines at distinct points is
called a “transversal” to the given lines. Quick Check
For examples, a road crossing two or more roads or a In the figure, the m l
railway line crossing several other lines are some examples line p cuts two lines p
l and m. Can you
of transversal lines. say, p is transversal
or not? ‘why’?
L D
P
C
In the adjoining figure, AB and CD are two lines and a line LM intersects
them at points Q and P, respectively. LM is called transversal line or A
Q
transversal. M
B
Angles made by a Transversal
In the adjoining figure, AB and CD are two lines and a line LM is a transversal that intersects them
at points Q and P, respectively.
L
The eight angles marked 1 to 8 have their special names: 4 1 D
1. Corresponding angles: The angles that lie on the same side of the C 3 2 P
transversal and in corresponding positions relative to the two lines (either
above the lines or below the lines) are called corresponding angles. A 8 5
In the adjacent figure, ∠1 and ∠5; ∠4 and ∠8; ∠2 and ∠6 and ∠3 and ∠7 7 6 Q B
are four pairs of corresponding angles.
M
Remember
A pair of corresponding angles:
• have different vertices.
• are on the same side of the transversal.
• are in corresponding positions relative to the two lines.
2. Alternate angles: A pair of angles that are on opposite sides of a transversal and have
different vertices are called alternate angles.
There are two types of alternate angles:
• Alternate interior angles: These angles are on opposite sides of the transversal and are
located between the two lines.
In the figure, ∠3 and ∠5, and ∠2 and ∠8 are the pairs of alternate interior angles.
• Alternate exterior angles: These angles are on the opposite sides of the transversal and are
located outside the two lines.
In the figure, ∠1 and ∠7, and ∠4 and ∠6 are the pairs of alternate exterior angles.
155 Lines and Angles
