Answer the 14th (a)."DON'T SEND STHE SIMILAR QUERIES.KINDLY PERFORM THE STEP BY STEP AND APPROPRIATE ANSWER".:



14. (a) In figure ( 1) given below, A BCD is a parallelogram and X is mid-point of BC. The line AX produced meets DC produced at Q. The parallelogram  ABPQ is completed. Prove that 
(i) the triangles ABX and QCX are congruent- 
(ii) DC=CQ=QP
 

Dear student

a)i) Consider ABX and QCXQXC=AXB      Vertically oppsote anglesQCX=ABX     alternate interior anglesBX=XC        X is the mid point of BCABX QCX    ASA criteriaii) Now since  ABX QCXAB=CQ    ...1     cpctAlso ABCD is a gmAB=CD   opposite sides are equal in a   gmCQ=CD   ....2   using 1Also ABPQ is a gmAB=PQ   opposite sides are equal in a   gmCQ=PQ      ....3  using 1So,  from 2 and 3 we haveCD=CQ=QPHence Proved.
Regards

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