Question

In Fig. 7.12, if AB ||DC and E is the mid - point of side AC, then prove that E is the mid-point of side BD.

Answer 1

In the given figure,$AB\parallel DC$

Hence,$\angle CDB=\angle DBA$ (Alternate angles)

Now in triangles DEC and BEA

$\angle DEC=\angle BEA$ (Vertically opposite angles)

$\angle CDB=\angle DBA$ (Proved above)

$EC=EA$ (E is midpoint of AC)

Hence, by AAS criterion triangle DEC $\cong$ triangle BEA

Then by c.p.c.t. $DE=BE$

Therefore E is the midpoint of BD