Question

In Fig. ABCD is a trapezium in which AB||DC. E is the mid-point of AD. A line l through E is parallel to AB show that l bisects the side BC.[3 MARKS]

Answer 1

Concept : 0.5 Mark
Construction : 0.5 Mark
Proof : 2 Marks


Join $DB$ and let it intersect the line $l$ at the point $G.$

Look at $\Delta DAB.$

$E$ is the midpoint of $AD$ and $EG\parallel AB.$

$\Rightarrow G$ is the midpoint of $DB$. [By converse of midpoint theorem]

Consider $\Delta BCD.$

$G$ is the midpoint of $BD$ and $GF\parallel DC.$

$\Rightarrow F$ is the midpoint of $BC$ . [By converse of midpoint theorem]

Hence, proved.