Triangles ABC and DEF are given in such a way that AB||DE; AB = DE; show that AC||DF and AC = DF.

Asked by Topperlearning User | 16th Aug, 2017, 03:10: PM

Expert Answer:

AB||DE; AB = DE       
So, ABED is a parallelogram.
Therefore, AD||BE and AD = BE  ...................................................(i)
BC||EF and BC = EF.
So,  BEFC is a parallelogram  
Therefore, CF||BE and CF = BE   ...................................................(ii)
From (i) and (ii) AD||CF and AD = CF
So,  ACFD is a parallelogram.
Hence,   AC||DF and AC = DF

Answered by  | 16th Aug, 2017, 05:10: PM