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Similar Triangles

Similar Triangles

Whenever we talk about two congruent figures then they have the ‘same shape’ and the ‘same size’. There are figures that are of the ‘same shape but not necessarily of the ‘same size’. They are said to be similar. Congruent figures are similar but the converse is not true

All regular polygons of same number of sides are similar. They are equilateral triangles, squares etc. All circles are also similar.

Two polygons of the same number of sides are similar if their corresponding angles are sides are proportional.

Two triangles are similar if their corresponding are equal and corresponding sides are proportional.

Basic Proportionality Theorem or Thales Theorem.

Theorem-1

If a line is drawn parallel to one side of a triangle, to interest the other two sides indistinct points, the other two sides are divided in the same ratio.

Given: - In 

To prove:- 

Construction:- BE and CD are joined.  and  are drawn.

Proof:-

But 

as they are on the same base DE and 

 from (1), (2) and (3) we get 

Corollary: In  then

Proof:- We know


(Taking reciprocals)

Multiplying (1) and (2) we get

 

 


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