ABCD is a parallelogram,P and Q are points on DC and AB respectively,such that angle DAP=angleBCQ.Show that Acqp is a parallelogram. Share with your friends Share 0 priyanka saggu answered this $Given:Aparalle\mathrm{log}ramABCD\phantom{\rule{0ex}{0ex}}ToProve:APCQisparalle\mathrm{log}ram.\phantom{\rule{0ex}{0ex}}Proof:\angle A=\angle C\phantom{\rule{0ex}{0ex}}\{Oppositeangleofparalle\mathrm{log}ramareequal\}\phantom{\rule{0ex}{0ex}}\angle DAP+\angle PAQ=\angle PCQ+\angle QCB\phantom{\rule{0ex}{0ex}}\angle PAQ=\angle PCQ\phantom{\rule{0ex}{0ex}}Whichisapairofoppositeangles\phantom{\rule{0ex}{0ex}}so,APCQisparalle\mathrm{log}ram.$ 9 View Full Answer Aishwarya Suresh answered this It is given that angDAP= angBCQ.But angDAP= ang APC ( alternate interior angles) andangBCQ= ang AQC (alternate interior angles)Therefore angAPC= ang AQCConsider Quadrilateral AQCP,Opposite angles i.e. ang APC and ang AQC are equal,Therefore,AQCP is a parallelogramProved!Thumbs up if you find it useful! 4 Aishwarya Suresh answered this 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p6, 5s2, 4d10, 5p2 -3