Question

The area of which of the following quadrilaterals are equal in the given figure if lines $AB$ is parallel to $HC$, $AH$ is parallel to $BG$ and $AD$ is parallel to $BC$?

• A. $HABC$ and $DABG$
• B. $DABG$ and $DABC$
• C. $HABC$ and $HABG$
• D. $DABC$ and $HABG$

Answer 1

The correct option is D $DABC$ and $HABG$

In quadrilateral DABC

$\because HC\parallel AB$ and

$AD\parallel BC$

$\therefore DC\parallel AB$

So,quadrilateral DABC is parallelogram.

Now, In quadrilateral HABG

$\because HC\parallel AB$ and

$HA\parallel BG$

$\therefore HG\parallel AB$

So,quadrilateral HABG is parallelogram.

WE shaw the DABG is trapezium becuase

$HC\parallel AB$

$\therefore DG\parallel AB$

so,$DE=GF$

Then,

Area of parallelogram $DABC=DE\times AB$

and Area of parallelogram $HABG=GF\times AB$

$\because DE=GF$

Area of parallelogram $HABG=DE\times AB$

So, $DABC=HABG$