Given the trapezoid $ABCD$ with EF as median, what is the measure of segment $PQ$? $AB = 16$ cm, $DC = 24$ cm and PQ lies on the median $EF$ being cut by diagonals $AC$ and $BD$.
I have been looking for any theorems on trapezoid for me to be able to answer this problem. I am only able to find the measure of segment by mere illustration. Is there any theorems that can help me answer this question?
Best Answer
Say we have points $E-P-Q-F$ on median and $E$ is on $AD$.
Then since $EP$ is median in $ACD$ we have $EP = CD/2$,
and $QF$ is median in $BCD$, so we have $QF = CD/2$.
So $$PQ = EF - EP-QF = {AB+CD\over 2}-CD = {AB-CD\over 2} = 4$$