GMAT Quant: Geometry – Lines

GMAT Quant analyses your mathematical skills based on many topics of Geometry like Triangle, Special Right Triangles, Area, Perimeter, and Volume of various geometrical shapes etc.

What is a Line?

A line is a series of joined dots that extend to infinity.

So, if a line has no end points, how do we operate over it?

We just take a segment of the line of some particular length that fulfills our requirements. These segments of lines are known as line segments.

Some special types of lines:

Parallel Lines

Two lines lying in the same plane yet never intersecting one another is said to be parallel lines. From the concept of co-ordinate geometry, two parallel lines will have the same slope but different intercepts related to the plane they are lying in. Whereas, non-parallel lines intersect one another at some point and have different slopes.

Perpendicular Lines

Perpendicular lines are intersecting lines that intersect at an exact angle of 90 Degrees.

These were some of the basic information about lines.

Let’s solve a question now:

If AB & ED are parallel to one another, then,

What is the value of angle C?

Solution:

Step1. As AB and ED are parallel,

So, angle EAO = angle AED = 65 degree

Step2. Angle OAE + angle EAD + angle DAB = 180 degree

So, angle DAB= 40 degrees

Step3. Angle CAB + angle ABC + angle BCA = 180 degree

So, angle C = 45 degree.

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