Geometry -concepts and properties for SSC CGL Tier-I Geometry is one of the most important topics of Quantitative Aptitude section of SSC CGL exam. It

York 2020-11-30 Answered
Geometry -concepts and properties for SSC CGL Tier-I Geometry is one of the most important topics of Quantitative Aptitude section of SSC CGL exam. It includes various concepts related to lines, angles, triangles, circles, polygons and so on. So, today I will just discuss concept and properties of triangle. Always remember that in Geometry, You need a very basic understanding. Cramming is not gonna help you anywhere.
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Answered 2021-04-21 Author has 162 answers

Triangles

=Figure with three sides.  Study the following triangle: A,B,C to points. a, b, c to sides. x, y, z to angles.
image
Perimeter of triangle =a+b+c
Remember that, Sum of all the angles is always 180
i.e. x+y+z=180

Classification of Triangles

Basically there are three types of triangles excluding right angle triangle. Let me tell you how they vary from each other.

  • Scalene Triangle
  • Isosceles Triangle
  • Equilateral Triangle

Scalene Triangle: No side of triangle is equal.
Isosceles Triangle: Two sides of triangle are equal.
Equilateral Triangle: All sides of triangle are equal.

  Scalene Isosceles Equilateral
Definition a ne b ne c ane b = c a = b = c
Area   A (b/4)4a2b2 (3)12(a2)/4
Height - (4a2b2)/2 (3)12a/2

A=s(sa)(sb)(sc)1/2
where, s=(a+b+c)/2

Properties of external angles of Triangle:

1. Sum of all exterior angles is 360
Study the following set of triangles and their exterior angles,
image
a, b, c to Interior angles. p, q, r and s, t, u to Exterior angles.
So, sum of exterior angles =360 i.e. p+q+r=360 and s+t+u=360
2. Next property of exterior angle which is important in paper point of view:

External angle = Sum of two internal angles.

For example: In above figures,
r=a+b
q=a+c
s=b+c and so on.

 

Right angle Triangle

Following triangle is a right angle triangle i.e. a triangle with one out of three 90 angle. image

 

 

 

Area of right angle triangle 

Area=12× Base times Perpendicular 

 

 

Example with Solution

 Example: In following figure, CE is perpendicular to AB, angle ACE=20 and angle ABD=50. Find angle BDA:
image
Solution: To Find: angle BDA
For this what we need --- angle BAD  Because, Sum of all angles =180
Consider, triangle ECA,
CEA+EAC+ACE=180 i.e. 90+20+EAC=180 Therefore, EAC=70
Now, come to triangle ABD,
ABD+BDA+BAD=180

70+50+BAD=180

Therefore, BAD=60
Example: In given figure. BC is produced to D and angle BAC=40 and angle ABC=70. Find angle ACD:
image
 Solution: In above figure, ACD is an exterior angle, and according to property, Exterior angle = Sum of interior angles Therefore, ACD=70+40=110
This is not the end of this chapter. These are just the basics. In next session, I will discuss some important results, properties (congruency, similarity) and much more. Always remember, Geometry needs practice and time.
 

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