Question

CDEF is a trapezium in which CD ∥ FE, CE is a diagonal and P is the

mid-point of CF. A line is drawn through P parallel to FE intersecting

DE at Q. Show that Q is the mid-point of DE.​

Answer 1

Answer:

Given: ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F.

To Prove: F is the mid-point of BC.

Proof: Let DB intersect EF at G.

In ∆DAB,

∵ E is the mid-point of DA and EG || AB

∴ G is the mid-point of D

| By converse of mid-point theorem

Again, in ∆BDC,

∵ G is the mid-point of BD and GF || AB || DC

∴ F is the mid-point of BC.

| By converse of mid-point theorem