Question

Question 9
In figure , AB ∥ DE, AB = DE, AC ∥ DF and AC = DF . Prove that BC ∥ EF and BC = EF.

Answer 1

Given in figure AB ∥ DE and AC ∥ DF. Also AB = DE and AC = DF

To Prove BC ∥EF and BC = EF

Proof in quadrilateral ABED,

AB ∥ DE and AB = DE

So, ABED is a parallelogram,

$\therefore$ AD ∥ BE and AD = BE …..(i)

Now, in quadrilateral ACFD,

AC ∥FD and AC = FD

Thus, ACFD is a parallelogram

$\therefore$ AD ∥ CF and AD = CF …(ii)

From eqs (i) and (ii),

AD = BE = CF and CF ∥ BE …….(iii)

Now, in quadrilateral BCFE.

BE = CF [from Eq. (iii)]

So, BCFE Is a parallelogram,

$\therefore$ BC=EF and BC ∥ EF Hence proved.