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If A B C and D E F are two triangles s...

If ` A B C` and ` D E F` are two triangles such that `A B ,B C` are respectively equal and parallel to `D E ,E F ,` then show that (i) quad ABED is a parallelogram (ii) quad BCFE is a paralellogram (iii) AC=DF (iv) ` Delta ABC cong Delta DEF`

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(i) Consider the quadrilateral ABED We have, AB=DE and AB∥DE
One pair of opposite sides are equal and parallel.
Therefore,ABED is a parallelogram.
(ii) In quadrilateral BEFC ,
we have BC=EF and BC ∥ EF.
One pair of opposite sides is equal and parallel. therefore, BEFC is a parallelogram.(III) Since ACFD is parallelogram.
AC=DF ∣ As Opposite sides of a parallelogram ACFD
(iV) In triangles ABC and DEF, we have AB=DE ∣ (opposite sides of ABED
BC=EF ∣ (Opposite sides of BEFC
and CA=FD Opposite. sides of ACFD.Using the SSS criterion of congruence,
`/_\ABC≅/_\DEF`
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