Question 1206184

given: Δ{{{ABC}}} ≅ Δ{{{DEF}}}
Prove Δ{{{ABC}}} ∼ Δ{{{GEC}}}

we need to show that the corresponding angles of these triangles are congruent

statement...................................reason
Δ{{{ABC}}} ≅ Δ{{{DEF}}}........................given (all their corresponding angles are congruent)
< {{{ABC}}} ≅ <{{{GEC}}}........................point{{{ C}}} is the intersection of lines {{{AG }}}and {{{BE}}},  and {{{GC}}} ||{{{ DF}}}, Alternate Interior Angles Theorem

< {{{DEF}}} ≅ < {{{GCE}}}......................point {{{E }}}is the intersection of lines {{{DG}}} and {{{BF}}}, and {{{CG}}} || {{{DF}}}, Alternate Interior Angles Theorem
  Δ{{{ABC}}} ∼ Δ{{{GEC}}}.....................by the angle-angle ({{{AA}}}) theorem