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In DeltaA B Cand DeltaD E F, A B\ =\ D E...

In `DeltaA B C`and `DeltaD E F`, `A B\ =\ D E`, `A B\ ||\ D E`, `B C\ =\ E F` and `B C\ ||\ E F`. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22).Show that
(i) quadrilateral ABED is a parallelogram
(ii) quadrilateral BEFC is a parallelogram
(iii) AD || CF and AD = CF
(iv) quadrilateral ACFD is a parallelogram
(v) AC = DF
(vi) ∆ ABC ≅ ∆ DEF.

Text Solution

Verified by Experts

(i) Given, AB = DE and AB ||DE
If one pair of opposite sides of a quadrilateral are equal and parallel to each other,
then it is a parallelogram.
Thus, quadrilateral ABED is a parallelogram.
(ii)Again, BC = EF and BC || EF
Therefore, quadrilateral BEFC is a parallelogram using the concept discussed in (i).
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