Question

$ABCD$ is parallelogram. $L$ and $M$ are points on $AB$ and $DC$ respectively such that $AL=CM$. The diagonal $BD$ intersects $LM$ at point $O$. If $AB=14textcm,AD=9\text{cm}$ and $LO=5\text{cm}$, find the length of $MO$.

Answer 1

Given : $ABCD$ is a parallelogram and $AL=CM$

To find : The length of $MO$

Solution:

$AB=CD$ (opposite sides of parallelogram)

Subtracting $AL$ from both sides

$AB-AL=CD-AL$

$AB-AL=CD-CM$ (because $AL=CM$)

$LB=DM$

In triangles $BLO$ and $MDO$,

$\angle MDO=\angle LBO$ (because $AB||CD$ and taking $DB$ as transversal)

$LB=DM$

$\angle OMD=\angle OLB$ (because $AB||CD$ and taking $ML$ as transversal)

So, by A.S.A criterion of congruency, triangle $BLO$ is congruent to triangle $MDO.$

Therefore,

$MO=LO=5\text{cm}$ (By CPCT)