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**Basics of Geometry**

**Angles**

Based on the measurement, angles have been classified into different groups.

**Complementary angles:**

Two angles taken together are said to be complementary if the sum of measurement of the angles equal to

90^{o}. If ∠ A + ∠ B = 90^{o} then ∠A is complementary of ∠B and vice – versa.

**Supplementary angles:**

Two angles are supplementary if sum of their measure is 180^{o}. If ∠ A + ∠ B = 180^{o} then ∠A is supplementary

of ∠B and vice – versa.

**Linear Pair:**

Two angle drawn on a same point and have one arm common. If sum of their measure equals to 180^{o}, then

they are said to be liner pair of angles.

∠AOP and ∠POB are linear pair of angles.

**Adjacent angles:**

Two angles are adjacent if and only if they have one common arm between them.

In the above figure, ∠ABC and ∠BCD are adjacent angles, since they have BC as their common arm.

**Properties of Lines**

A line consists of infinite dots. A line is drawn by joining any two different points on a plane. Two different lines

drawn can be either parallel or intersecting depending on their nature.

If two lines intersect at a point, then they form two pairs of opposite angles (as shown in the figure), which are

known as vertically opposite angles and have same measure. In the figure, ∠PRQ and ∠SRT are vertically

opposite angles. Also ∠QRS and ∠PRT are vertically opposite angles.

x

Also, ∠x + ∠y = 180^{o} and are Linear pair angles.

**Perpendicular Lines:**

An angle that has a measure of 90^{o} is a right angle. If two lines intersect at right angels, the lines are

perpendicular. For example:

L1 and L2 above are perpendicular and denoted by L1 ⊥ L2.

**Parallel Lines:**

Two lines drawn on a plane are said to be parallel if they do not intersect each other. In figure below lines, L1

and L2 are parallel and denoted by L1??L2

**Parallel lines and a transverse:**

If a common line intersects two parallel lines L1 and L2, then that common line is known as transverse.

Pair of corresponding angles = (∠1 & ∠5) and (∠4 & ∠ 6)

Pair of internal alternate angles = (∠2 & ∠5)

Pair of exterior alternate angles = (∠3 & ∠6)

Vertically opposite angles = ∠3 & ∠4

For parallel lines intersected by the transversal, the pair of corresponding angles, interior alternate angles and

exterior alternate angles are equal.

∠1 = ∠5, ∠2 = ∠5, ∠3 = ∠6 and ∠3 = ∠4

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