Basics of Geometry - Examples (with Solutions), Geometry, Quantitative Reasoning Government Jobs Notes | EduRev
Quantitative Aptitude for Banking Preparation
UPSC : Basics of Geometry - Examples (with Solutions), Geometry, Quantitative Reasoning Government Jobs Notes | EduRev
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
90o. If ∠A + ∠B = 90o then ∠A is complementary of ∠B and vice – versa.
Supplementary angles:
Two angles are supplementary if sum of their measure is 180o. If ∠A + ∠B = 180o 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 180o, 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 = 180o and are Linear pair angles.
Perpendicular Lines:
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.
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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