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Draw two lines on a plane. They can be either parallel or intersecting.

**Geometry Basics â€“Recall**

Draw two lines on a plane. They can be either
parallel or intersecting.

**Parallel
lines** Two or more lines lying in
the same plane that never meet.

**Intersecting
lines** Two lines which meet at a common
point.

**Perpendicular
lines **Two lines which intersect each other at right angle.

**Concurrent
lines** Three or more lines passing
through the same point.

Plumbers measure the angle between connecting pipes
to make a good fitting. Wood workers adjust their saw blades to cut wood at the
correct angle. Air Traffic Controllers (ATC) use angles to direct planes. Carom
and billiards players must know their angles to plan their shots. An angle is
formed by two rays that share a common end point provided that the two rays are
non-collinear.

Two angles are Complementary if their sum is 90Â°.
For example, if âˆ ABC=64Â° and âˆ DEF=26Â°, then angles âˆ ABC and âˆ DEF are complementary to each other
because âˆ ABC + âˆ DEF = 90Â°

Two angles are Supplementary if their sum is 180Â°.

For example if âˆ ABC=110Â° and âˆ XYZ=70Â°

Here âˆ ABC + âˆ XYZ = 180Â°

âˆ´âˆ ABC and âˆ XYZ are supplementary to each other

Two angles are called adjacent angles if

i. They have a common vertex

ii. They have a common arm.

iii. The common arm lies between the two non-common arms.

If a ray stands on a straight line then the sum of
two adjacent angle is 180Â°. We then say that the angles so formed is a linear
pair.

âˆ AOC + âˆ BOC=180Â°

âˆ´âˆ AOC and âˆ BOC form a linear pair

âˆ XOZ + âˆ YOZ = 180Â°

âˆ XOZ and âˆ YOZ form a linear pair

If two lines intersect each other, then vertically
opposite angles are equal.

In this figure âˆ POQ = âˆ SOR

âˆ POS = âˆ QOR

A line which intersects two or more lines at a
distinct points is called a transversal of those lines.

Case (i) When a
transversal intersect two lines, we get eight angles.

In the figure the line *l* is the transversal for the lines *m *and* n*

(i) Corresponding Angles: âˆ 1 and âˆ 5, âˆ 2 and âˆ 6, âˆ 3 and âˆ 7, âˆ 4 and âˆ 8

(ii) Alternate Interior Angles: âˆ 4 and âˆ 6, âˆ 3 and âˆ 5

(iii) Alternate Exterior Angles: âˆ 1 and âˆ 7, âˆ 2 and âˆ 8

(iv) âˆ 4 and âˆ 5,âˆ 3 and âˆ 6 are interior angles on the same
side of the transversal.

(v) âˆ 1 and âˆ 8, âˆ 2 and âˆ 7 are exterior angles on the same
side of the transversal.

Case (ii) If a
transversal intersects two parallel lines. The transversal forms different
pairs of angles.

Two triangles are congruent if the sides and angles
of one triangle are equal to the corresponding sides and angles of another
triangle.

Tags : Mathematics , 9th EM Mathematics : Geometry

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