Thursday, 3 August 2017

Triangle IX - Top 2 Triangle Theorems to Remember for SSC Exams

In this post, we discuss triangle theorems such as Basic Proportionality Theorem and Midpoint Theorem that will help solve geometric questions asked in SSC Exams.

Triangle Theorems

Triangle theorems come in handy when an SSC Aspirant is solving geometric questions. Triangle theorems such as Pythagoras theorem, Basic proportionality theorem, and Midpoint theorem are a few basic triangle theorems that a candidate attempting any competitive exams should know.

Previously, we have discussed Pythagoras theorem. In this post, we will discuss Basic Proportionality theorem and Midpoint theorem that will help you crack SSC Exams.

Triangle Theorem 1: Basic Proportionality Theorem

In any triangle, if we draw a line parallel to any side of the triangle then the parallel line will divide the other two sides in a particular ratio.

Example:
In a triangle ABC,

PQ is the parallel line to the Base BC

Triangle Theorems
Triangle Theorems
EF is the parallel line to the side AC

Triangle Theorems
Triangle Theorems

Triangle Theorem 1: Midpoint Theorem

The line joining the midpoint of any two sides of a triangle will always be parallel to the third side and its length will be half of the length of the third side.

In triangle ABC,

P and Q are the two mid-point on the sides AB and AC
(i) PQ// BC 
(ii) PQ = ½ BC

Triangle Theorems
Triangle Theorems

Likewise,

M and Q are the two mid-point on the sides AC and CB
(i) MQ// AB
(ii) MQ = ½ AB

Triangle Theorems
Triangle Theorems
P and M are the two mid-point on the sides AB and BC
(i) PM// AC
(ii) PM = ½ AC

Triangle Theorems
Triangle Theorems

The triangle obtained by joining the three sides of the triangle is 1/4th in the area of the original triangle.
PQM = 1/4th ABC

Triangle Theorems
Triangle Theorems

Hope you have thoroughly understood triangle theorems as often these triangle theorems are used to attempt geometric questions.

Do write in the comment section below on how these triangle theorems have helped you solve geometric questions.

Triangle theorems
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