Basics of Geometry - Examples (with Solutions), Geometry, Quantitative Reasoning Government Jobs Notes | EduRev

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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
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.

Basics of Geometry - Examples (with Solutions), Geometry, Quantitative Reasoning Government Jobs Notes | EduRev

∠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.

Basics of Geometry - Examples (with Solutions), Geometry, Quantitative Reasoning Government Jobs Notes | EduRev

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.

Basics of Geometry - Examples (with Solutions), Geometry, Quantitative Reasoning Government Jobs Notes | EduRev x
Also, ∠x + ∠y = 180o and are Linear pair angles.

Basics of Geometry - Examples (with Solutions), Geometry, Quantitative Reasoning Government Jobs Notes | EduRev

 

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:

Basics of Geometry - Examples (with Solutions), Geometry, Quantitative Reasoning Government Jobs Notes | EduRev

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

Basics of Geometry - Examples (with Solutions), Geometry, Quantitative Reasoning Government Jobs Notes | EduRev

 

Parallel lines and a transverse:

If a common line intersects two parallel lines L1 and L2, then that common line is known as transverse.

Basics of Geometry - Examples (with Solutions), Geometry, Quantitative Reasoning Government Jobs Notes | EduRev

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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