In a trapezium ABCD, AB||CD, angle B = 1/2D. If AD = q and DC = p, find AB.

Question

In a trapezium $ABCD$, $AB||CD$, angle$B$ = $\frac{1}{2}D$. If $AD = q$ and $DC = p$, find $AB$.

Answer 1

Draw the bisector of angle D, which must be parallel to BC to meet AB at X. Triangle AXD is isosceles, and XBCD is a parallelogram,so $AX + XB = AB= p+q$