Question

In quadrilateral ABCD, BM and DN are drawn perpendiculars to AC such that BM = DN. If BR = 8 cm, then find BD.

Answer 1

Given$ABCD$ is a quadrilateral in which diagonals $AC$ and $BD$ intersect each other at $P$

Also,$DN\perp AC$ and $BM\perp AC$

$DN=BM$

In $△DNP$ and $△BMP$ we have

$\angle DPN=\angle BPM$ since they are vertically opposite angles.

$\angle DNP=\angle BMP$ since each are equal to ${90}^{\circ }$

$DN=BM$(given)

$\Rightarrow △DNP\cong △BMP$ by AAS postulate.

$\Rightarrow DP=BP=8$cms by CPCT

We have $BD=BP+DP=8+8=16$cms from the diagram.