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

CBSE Class 10 board exams from February 15 to March 18; download date sheet 2025 PDF
anam-khan

CBSE Date Sheet 2025 Live: CBSE Class 10, 12 board exam timetable soon at cbse.gov.in; practical dates
anam-khan

CBSE Date Sheet 2025 Live: CBSE to announce Class 10, 12 board exam dates soon at cbse.gov.in; sample paper

Latest Question