Question

ABCD is a rhombus and AB is produced to E and F such that AE = AB = BF. Prove that ED and FC are perpendicular to each other.

Answer 1

Given : ABCD is a rhombus. AB produced to E and F such that AE = AB = BF

Construction : Join ED and CF and produce it to meet at G.

To : ED⟂FCprove

Proof : AB is produced to points E and F such that.

AE = AB = BF  .....(i)

Also, since ABCD is a rhombus

AB = CD = BC = AD ...(ii)

Now, in ΔBCF, BC = BF [From (i) and (ii)]

[∠4 and ∠3 are consecutive interior angles]

Hence proved.