Question

in quadrilateral ABCD side BC parallel sideAD . segment AC and BD intersect in point Q if AQ equal to 1 by 3 of AC then show that DQ equal to 1 by 2 of BQ

Answer 1

Here triangle AOD is similar to Triangle CQB. Therefore A Q by CQ equal to QD by QB is equal to ad by cd (1)

. according to questionAQ=1/3AC

=>AQ=1/3 (AQ+QC)

FROM 1.

{1/3 (AQ+QC)}/CQ=QD/QB=>

1/3(AQ/QC)+1/3(QC/QC)=QD/QB

=>1/3(QD/QB)+1/3=QD/QB

=>1/3=2/3 (QD/QB)

QD=1/2QB

PROVED