Hi, here is your answer
sol:
Given: ABCD is a trapezium.
To Prove: DE/EB = CE /EA
Construction: Draw EF || BA || CD, intersecting AD in F.
Proof:
FE || AB (Given)
DE/EB = DF/FA [According to basic proportionality theorem] --------- (1)
FE || DC (Given)
CE/EA = DF/FA [According to basic proportionality theorem] --------- (2)
From (1) and (2), we get
DE/EB = CE/EA
So, diagonals of a trapezium divide each other proportionally.
Written on Feb. 5, 2019, 8:44 p.m.