Question

AB and CD are two parallel lines the a transversal intersects AB at C and CD at Y. Prove that the bisector of the interior and form a rectangle.

Answer 1

given -two parallel lines AB and CD are intersect the transversal L at P and R
PQ, RQ, RS, PS are bisector of APR and PRC
prove that -PQRS is a rectangle
proof - since AB parallel CD and L is transversal
angle APR =PRD (alt interior angle)
1/2APR = 1/2PRDb
QPR =PRS
But these are all interior angle
PQ parallel RS similarly QR parallel PS
so PQRS is a parallogram
now ray stands on AB, 1/2 APR +1/2BPR=90
QPR +SPR =90
QPS =90
thus PQRS is a parallogram no. of whose angle is 90
hence PQRS is a rectangle