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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.
1380272_f1fe01e2fbfe40469fefe64b4bfc1310.png

Solution
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In the given figure,ABDC
Hence,CDB=DBA (Alternate angles)
Now in triangles DEC and BEA
DEC=BEA (Vertically opposite angles)
CDB=DBA (Proved above)
EC=EA (E is midpoint of AC)
Hence, by AAS criterion triangle DEC triangle BEA
Then by c.p.c.t. DE=BE
Therefore E is the midpoint of BD

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