Q

# In ∆ ABC and ∆ DEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22). Show that (iv) quadrilateral ACDF is a parallelogram.

Q : 11         In $\small \Delta ABC$ and $\small \Delta DEF$, $\small AB=DE,AB\parallel DE,BC=EF$ and $\small BC\parallel EF.$.  Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. $\small 8.22$). Show that

(iv) quadrilateral ACFD is a parallelogram

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To prove :  quadrilateral ACFD is a parallelogram

Proof :

In ABED,

In BEFC,

BE=CF.................3(BEFC is a parallelogram)

BE||CF .................4(BEFC is a parallelogram)

From 2 and 4 , we get

From 1 and 3, we get

From 5 and 6, we get

Thus, quadrilateral ACFD is a parallelogram

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