Answer the 12th question."DON'T SEND THE SIMILAR QUERY,KINDLY PERFORM THE CORRECT AND STEP BY STEP CALCULATION".

Answer the 12th question."DON'T SEND THE SIMILAR QUERY,KINDLY PERFORM THE CORRECT AND STEP BY STEP CALCULATION". (it) Prove that bisectors of any two opposite angles or a (iiJ) If the diagonals of a quadrilateral are equal and bisect each other at right then prove that it is a square. 12- (i) [f ABCD is a rectangle in which the diagonal BD bisects Z B, then show that is a square. (iO Show that if the diagonals of a quadrilateral are equal and bisect each other at • angles, then it is a square. 13. P and Q are points On opposite sides AD and BC of a parallelogram ABCD such PQ passes through the point of intersection O of its diagonals AC and BD. Show that is bisected at O. Hint: Show that AOAP AOCQ. 14. (a) In figure (1) given below, ABCD is a parallelogram and X is nmid-point of BC 111 line AX produced meets DC produced at Q. The parallelogram ABPQ is complete Prove that (i) the triangles ABX and QCX are congruent. (ii)DC QP (b) In figure (2) given below, points P and Q have been taken on opposite sides ABS CD respectively of a parallelogram ABCD such that AP = CQ. Show that AC PQ bisect each other. B Q c