Question

ngles of
agle.
gles, then
In ∆ABC and ∆DEF, AB=DE,AB || DE, BC=EFand BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22).
Show that
(1) quadrilateral ABED is a parallelogram
(ii) quadrilateral BEFC is a parallelogram
(ii) AD || CF and AD=CF
(iv) quadrilateral ACFD is a parallelogram
(v) AC=DF
(vi) ∆ABC =~(congruent) ∆DEF.
​

Answer 1

$\huge{\red{Answer:-}}$

(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,

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 AD || CF

________________________

(iv) As we had 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

_________________________

(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)

=========================

Thanks!!❤️

Answer 2

Answer:

(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 are equal and parallel.therefore ,BEFC is a parallelogram.

(iii) AD=BE and AD∥BE ∣ As ABED is a ||gm ... (1)

and CF=BE and CF∥BE ∣ As BEFC is a ||gm ... (2)

From (1) and (2), it can be inferred

AD=CF and AD∥CF

(iv) AD=CF and AD∥CF

One pair of opposite sides are equal and parallel

⇒ ACFD is a parallelogram.

(v) Since ACFD is parallelogram.

AC=DF ∣ As Opposite sides of a|| gm ACFD

(vi) 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 SSS criterion of congruence,

△ABC≅△DEF