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 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