# Quant Ability Study Material for MBA Exams

# Geometry Basics

Geometry is branch of mathematics concerned with shapes, sizes and properties of figures. Geometry includes knowledge of angles, lines, triangles, quadrilaterals, circles and polygons.

### 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°. If ∠A + ∠B = 90°, then ∠A is complementary of ∠B and vice – versa.

**Supplementary angles:** Two angles are supplementary if sum of their measure is 180°. If ∠ A + ∠ B = 180°, 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°, then they are said to be liner pair of angles.

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

### 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, 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.

Also, ∠x + ∠y = 180° and are Linear pair angles.

**Perpendicular Lines**

An angle that has a measure of 90° is a **right angle**. If two lines intersect at right angels, the lines are perpendicular.

**Parallel Lines**

Two lines drawn on a plane are said to be parallel if they do not intersect each other.

**Parallel Lines and Transverse**

If a common line intersects two parallel lines L_{1} and L_{2}, 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