Question

D, E, F are the mid-point of the sides BC, CA and AB respectively of $\Delta ABC,then\Delta DEF$ is congruent to triangle

• A. ABC
• B. AEF
• C. BFD, CDE
• D. AFE, BFD, CDE

Answer 1

The correct option is D

AFE, BFD, CDE

In $\Delta ABC,D,E,F$ are the mid-points of the sides BC, CA, AB respectively DE, EF and FD are joined

$\because \text{E and F ar the mid-points AC and AB.}$

$\therefore EF=\frac{1}{2}BCandEF||BC$

Similarly, $DE=\frac{1}{2}ABandDE||AB$

$DF=\frac{1}{2}ACandDF||AC$

$\therefore \Delta DEF\text{is congruent to}\Delta AFE,\Delta BFD,\Delta CDE$