Question

State true or false:

The alongside figure shows a parallelogram $ABCD$ in which $AE=EF=FC$, then

$DE$ is parallel to $FB$

• A. True
• B. False

Answer 1

The correct option is A True

Between $△$ ADE and $△$ FBC

AE = FC (given)

$\angle DAE=\angle FCB$ ( because AD$\parallel$ BC)

AD = BC

So,$△$ ADE $\cong$ $△$ FBC

$\Rightarrow$ DE = BF

$\angle ADE=\angle FBC$

$\angle AED=\angle BFC$ ( above and $\angle DAE=\angle FCB$)

Then we can also write $\angle DEF=\angle BFE$ (${180}^o$ principle)

Hence DE $\parallel$ BF.