Question

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. Show that F is the mid-point of BC.

Answer 1

Data: 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: Straight line EF cuts at G.

In ∆ABD, E is the mid-point of AD (Data) 

EF || AB 

EG || AB 

∴ G is the mid-point of BD. 

∵ Converse of mid-point formula. 

DC || AB and EF || AB 

⇒ DC || EF 

In ∆BDC, 

GF || DC G is the mid-point of BD (proved) 

∴ F is the mid-point of BC.