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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 âˆ A + âˆ B = 90^{o} then âˆ A is complementary of âˆ B and vice â€“ versa.

**Supplementary angles:**

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

of âˆ B and vice â€“ 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.

âˆ AOP and âˆ 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, âˆ ABC and âˆ 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, âˆ PRQ and âˆ SRT are vertically

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

x

Also, âˆ x + âˆ 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 âŠ¥ 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 = (âˆ 1 & âˆ 5) and (âˆ 4 & âˆ 6)

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

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

Vertically opposite angles = âˆ 3 & âˆ 4

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

exterior alternate angles are equal.

âˆ 1 = âˆ 5, âˆ 2 = âˆ 5, âˆ 3 = âˆ 6 and âˆ 3 = âˆ 4

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