# In Δ ABC and Δ 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(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) Δ ABC ≅Δ DEF.

(i) Given that: AB = DE and

AB || DE

If two opposite sides of a quadrilateral are equal and parallel to each other, then it will be a parallelogram.

Therefore, quadrilateral ABED is a parallelogram

(ii) Again,

BC = EF and BC || EF

Therefore, quadrilateral BCEF is a parallelogram

(iii) As we had observed that ABED and BEFC are parallelograms

Therefore,

(Opposite sides of a parallelogram are equal and parallel)

And,

BE = CF and BE || CF

(Opposite sides of a parallelogram are equal and parallel)

ACFD are equal and parallel to each other, therefore, it is a parallelogram

(v) As ACFD is a parallelogram, therefore, the pair of opposite sides will be equal and parallel to each other

AC || DF and AC = DF

(vi) ΔABC and ΔDEF,

AB = DE (Given)

BC = EF (Given)

AC = DF (ACFD is a parallelogram)

ΔABC ΔDEF (By SSS congruence rule)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Properties of Parallelogram31 mins
Critical Thinking Problems on Quadrilaterals44 mins
Quiz | Basics of Quadrilaterals36 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses