Question

in figure a b parallel to BC and a b is equal to b and ac parallel to EF and ac is equal to AC prove that BC parallel to EF and BC is equal to EF​

Answer 1

Step-by-step explanation:

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.

AD || BE and AD = BE

Now, in quadrilateral ACFD,

AC || FD and AC = FD …..(i)

Thus, ACFD is a parallelogram.

AD || CF and AD = CF …(ii)

From Eqs. (i) and (ii),

AD = BE = CF and CF || BE …(iii)

Now, in quadrilateral BCFE,

BE = CF and BE||CF [from Eq. (iii)]

So, BCFE is a parallelogram. BC = EF and BC|| EF . Hence proved.

Answer 2

Step-by-step explanation:

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.

AD || BE and AD = BE

Now, in quadrilateral ACFD,

AC || FD and AC = FD …..(i)

Thus, ACFD is a parallelogram.

AD || CF and AD = CF …(ii)

From Eqs. (i) and (ii),

AD = BE = CF and CF || BE …(iii)

Now, in quadrilateral BCFE,

BE = CF and BE||CF [from Eq. (iii)]

So, BCFE is a parallelogram. BC = EF and BC|| EF .

Hence proved.