. In A ABC and A DEF, AB = DE, AB 11 DE, BC = EF and BC II EF. rtices A. B and C are joined to vertices D, E and F respectively (see figure ). Show that (i) quad rilateral ABED is a parallelogram --- 0 (ii) quad rilateral BEFC is a . . ---- ---- paro/Jelogram 8 c•- ----- (iU) AD 11 CF and AD = CF ----------e ---- F (iv) quadrilaU!ral ACFD is a paralJe/,ogram (v) AC = DF (vi) AABC :A DEF.

Consider quadrilateral ABED, AB = DE and AB 11 DE [Given] => ABED is a parallelogram. [In a quadrilateral if a pair of opposite sides is equal and parallel, then it is a parallelogram.] (ii) Consider quadrilat.eral BEFC, BC = EF and BC 11 EF [Given] => BEFC is a parallelogram. [Reason same as above] (iii) From result (i), ABED is a parallelogram. AD II BE and AD = BE From result (ii), BEFC is a parallelogram. BE II CF and BE = CF 116 AD II CF end AD = CF. . [From results (i) end (ii)] (iv) As AD II CF end AD = CF [From result (iii)] :. Quadrilat.eral ACFD is a parallelogram. (v) AC = DF. [•: ACFD is a parallelogram, result (iv)] (vi) Consider triangles ABC end DEF, AB = DE BC = EF AC = DF • ABC ::11 DEF. [Given] [Given]