Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If the areas of two similar triangles are equal, prove that they are congruent.

Q4   If the areas of two similar triangles are equal, prove that they are congruent.

Answers (1)

best_answer

Let \triangle ABC\, \sim \, \triangle DEF, therefore,

ar(\triangle ABC\,) = \,ar( \triangle DEF)                (Given )

\frac{ar(\triangle ABC)}{ar(\triangle DEF)}=\frac{AB^2}{DE^2}=\frac{BC^2}{EF^2}=\frac{AC^2}{DF^2}................................1

\therefore \frac{ar(\triangle ABC)}{ar(\triangle DEF)}=1

\Rightarrow \frac{AB^2}{DE^2}=\frac{BC^2}{EF^2}=\frac{AC^2}{DF^2}=1

AB=DE

BC=EF

AC=DF

\triangle ABC\, \cong \, \triangle DEF                    (SSS )

 

 

 

 

 

Posted by

seema garhwal

View full answer

Similar Questions

Trending Articles/News

anam-khan

Board Exams Date Sheet 2025 Live: RBSE 10th, 12th exams from March 6; CBSE admit card expected by month-end

Latest Question