Theorem 5: One Pair of Opposite Sides Parallel and Equal
Question 11 i...
Question
Question 11 (iv)
In ΔABCandΔDEF ,AB=DE, AB || DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that Quadrilateral ACFD is a parallelogram.
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Solution
It can be observed that ABED is a parallelogram (AB =DE, AB||DE) and BEFC is also a parallelogram (BC = EF, BC||EF) Therefore,
AD=BE and AD || BE
(Opposite sides of a parallelogram are equal and parallel)
And, BE=CF and BE || CF
(Opposite sides of a parallelogram are equal and parallel)
AD = CF and BE || CF
As we have observed that one pair of opposite sides (AD and CF) of quadrilateral ACFD are equal and parallel to each other, therefore, it is a parallelogram.