in the given figure ABCD and BPQ are lines. BP=BC and DQ|| CP. Prove that
a. CP = CD
b. DPbisects <CDQ

Dear Student,
Please find below the solution to the asked query:

As BP=BCBPC=PCBAs exterior angle is equal to sum of two opposite interior angles.BPC+PCB=4xBPC+BPC=4x2BPC=4xBPC=2x=PCBNow DQCPQDC=PCB Corresponding anglesQDC=2xAs exterior angle is equal to sum of two opposite interior angles.PCB=CPD+PDC2x=x+PDCPDC=xAs QDC=2x and PDC=xDP bisects CDQ Hence ProvedAs PDC=x and CPD and since sides opposite to equal angles are equal, henceCP=CD Hence Proved

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