wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Question 11 (iv)
In ΔABC and ΔDEF ,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.

Open in App
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.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon