CRE Vertices A. B snd C we joined toand ncvertices D. E and F respeeti

1.	CRE Vertices A. B snd C we joined toand ncvertices D. E and F respeetively (see Fig, 8 22),show thatquadrilateral ABED isa pirullek ramk) quad(a) ADICP and AD-CPàv) quadrilateral ACFD is a parallelogramIrilateral BEFC is a parallelogramFg. 822(v) AC DF
Answer» i) In quadrilateral ABED, AB = DE and AB \|\| DE (given) So,quadrilateral ABED is a parallelogram [Since a pair of opposite side isequal and parallel] (ii) In quadrilateral BEFC Again BC = EF andBC \|\| EF. so,quadrilateral BEFC is a parallelogram. [Since a pair of opposite side isequal and parallel] (iii)Since ABED and BEFC are parallelograms. AD = BE and BE = CF (Opposite sides of a parallelogram are equal) Thus, AD = CF. Also, AD \|\| BE and BE \|\| CF (Oppositesides of a parallelogram are parallel) Thus, AD \|\|CF Hence , AD\|\|CF & AD= CF (iv)AD and CF are opposite sides of quadrilateral ACFDwhich are equal and parallel to each other. Thus, AFCD it is a parallelogram. (v) Since, ACFD is a parallelogram. AC \|\| DF and AC=DF (vi) In ΔABC and ΔDEF, AB = DE (Given) BC = EF (Given) AC = DF (Opposite sides of a parallelogram) Thus, ΔABC ≅ ΔDEF (by SSS congruence rule)

CRE Vertices A. B snd C we joined toand ncvertices D. E and F respeetively (see Fig, 8 22),show thatquadrilateral ABED isa pirullek ramk) quad(a) ADICP and AD-CPàv) quadrilateral ACFD is a parallelogramIrilateral BEFC is a parallelogramFg. 822(v) AC DF

Answer»

In quadrilateral ABED,

AB = DE and AB || DE

(given)

So,quadrilateral ABED is a parallelogram

[Since a pair of opposite side isequal and parallel]

(ii) In quadrilateral BEFC

Again BC = EF andBC || EF.

so,quadrilateral BEFC is a parallelogram.

[Since a pair of opposite side isequal and parallel]

(iii)Since ABED and BEFC are parallelograms.

AD = BE and BE = CF (Opposite sides of a parallelogram are equal)

Thus, AD = CF.

Also, AD || BE and BE || CF

(Oppositesides of a parallelogram are parallel)

Thus, AD ||CF

Hence , AD||CF & AD= CF

(iv)AD and CF are opposite sides of quadrilateral ACFDwhich are equal and parallel to each other.

Thus, AFCD it is a parallelogram.

(v) Since, ACFD is a parallelogram.

AC || DF and AC=DF

(vi) In ΔABC and ΔDEF,

AB = DE (Given)

BC = EF (Given)

AC = DF (Opposite sides of a parallelogram)

Thus, ΔABC ≅ ΔDEF (by SSS congruence rule)