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QUADRILATERALS, 147, 9. In parallelogram ABCD, two points Pand Q are, taken on diagonal BD such that DP = BQ, (see Fig. 8.20). Show that:, 0 AAPD=ACQB, (i) AP=CQ, (iii) AAQB=ACPD, (iv) AQ=CP, (v) APCQİ a parallelogram, Fig. 8.20, 10. ABCD is a parallelogram and AP and CQ are, perpendiculars from vertices A and C on diagonal, BD (see Fig. 8.21). Show that, ΔΑΡΒ Δ CD, (i) AP=CQ, D, Fig. 8.21, ERT, 11. In A ABC and ADEF, AB = DE, AB || DE, BC=EF, and BC || EF. Vertices A, B and C are joined, vertices D, E and F respectively (see Fig, 8, Show that, @ quadrilateral ABED is a parallelogram, (i) quadrilateral BEFC is a parallelogram, (i) AD || CF and AD=CF, oeversubiched, (iv) quadrilateral ACFD is a parallelogram, Fig. 8.22, (v) AC=DF, (vi) A ABC=ADEF., 12. ABCD is a trapezium in which AB || CD and, AD = BC (see Fig. 8.23). Show that, O ZA=ZB, (i) 2C=ZD, (iii) A ABCA BAD, (iv) diagonal AC= diagonal BD, Fig. 8.23