Basics of Geometry
Based on the measurement, angles have been classified into different groups.
Two angles taken together are said to be complementary if the sum of measurement of the angles equal to
90o. If ∠ A + ∠ B = 90o then ∠A is complementary of ∠B and vice – versa.
Two angles are supplementary if sum of their measure is 180o. If ∠ A + ∠ B = 180o then ∠A is supplementary
of ∠B and vice – versa.
Two angle drawn on a same point and have one arm common. If sum of their measure equals to 180o, then
they are said to be liner pair of angles.
∠AOP and ∠POB are linear pair of 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.
Also, ∠x + ∠y = 180o and are Linear pair angles.
An angle that has a measure of 90o 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.
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