Question

$D,E,F$ are the mid points of the sides $AB,BC,CA$ respectively of $△ABC$. Then $△DEF$ is congruent to

• A. $△ABC$
• B. $△AEF$
• C. $△BDF,△CDE$
• D. $△ADF$

Answer 1

The correct option is D $△ADF$

Given: $△ABC$, $D,EandF$ are mid points of $AB,BC,CA$ respectively.
In $△ABC$

$F$ is mid point of $ACandD$ is mid point of $AB.$

Thus, By Mid point theorem

$FD=\frac{1}{2}CB$ and $FD=CB$ or $FD=CE$ and $FD\parallel CE$ ....(1)

Similarly,
$DE=FC$ and $DE\parallel FC$ ...(2)

$FE=DB$ and $FE\parallel DB$ ...3)

From (1), (2) and (3)

$\square ADEF$, $\square DBEF$, $\square DECF$ are parallelograms

The diagonal of a parallelogram divides the parallelogram into two congruent triangles.

Hence, $△DEF\cong △ADF$

$△DEF\cong △DBE$

$△DEF\cong △FEC$

$△DEF\cong △ADF\cong △ECF\cong △ADF$