D,E and F are the mid point of ides AB, BC, and AC resp . CG is drawn parallel to BA and meet DF produced in G . prove that triangle DEF is congruent to triange FCG .

Proof: ADF and CFG1=2 (alt interior angles)AF = FC(F is mid point of AC)3 =4 (vertically opposite angle)ADFCFG (ASA)DF = FG (CPCT)------(1)DEF and FCGDF = FGDE = FC(by mid point theorem)5 =4DEFFCG (SAS)

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