19. In the given figure, the side AC of aAABC is produced to E such th

1.	19. In the given figure, the side AC of aAABC is produced to E such thatCE AC. If D is the mid-point of BCand ED produced meets AB at F and CP,DQ are drawn parallel to BA. Prove thatF2BQuadrilaterals
Answer» Given,ABC is a triangle.D is midpoint of BC and DQ.They're drawn parallel to BA. Then, Q is midpoint of AC.∴AQ = DC ∴ FA parallel to DQ\|\|PC.AQC, is a transversal so, AQ = QC and FDP also a transveral on them. ∴FD = DP .......(1) [intercept theorem]EC = 1/2 AC = QC Now, triangle EQD, here C is midpoint of EQ and CP which is parallel to DQ.And, P is midpoint of DE.DP = PE..........(2) Therefore, From (1) and (2)FD = DP = PE∴ FD = 1/3 FE

19. In the given figure, the side AC of aAABC is produced to E such thatCE AC. If D is the mid-point of BCand ED produced meets AB at F and CP,DQ are drawn parallel to BA. Prove thatF2BQuadrilaterals

Answer»

Given,ABC is a triangle.D is midpoint of BC and DQ.They're drawn parallel to BA.

Then, Q is midpoint of AC.∴AQ = DC

∴ FA parallel to DQ||PC.AQC, is a transversal so, AQ = QC and FDP also a transveral on them.

∴FD = DP .......(1) [intercept theorem]EC = 1/2 AC = QC

Now, triangle EQD, here C is midpoint of EQ and CP which is parallel to DQ.And, P is midpoint of DE.DP = PE..........(2)

Therefore, From (1) and (2)FD = DP = PE∴ FD = 1/3 FE