Look at the figure below:

triangle efd has the measure of angle efd equal to 60 degrees. g is a point on side df. points e and g are joined by a straight line. angle deg measures 60 degrees.

make a two-column proof showing statements and reasons to prove that triangle def is similar to triangle dge.

Let's compare the Angles in both triangle DEF & DEG

Triangle DEF     Triangle DEG
         
Angle EDF           =     Angle EDF
Angle EFG           =     Angle DEG = 60° (given)
Hence Angle DEF =    Angle EGD (the sum of all angles in a triangle =180°
Proof : Angle(EDF+EFG+DEF = EDF+DEG+EGD = 180°

ANGLE(EDF+60°+EGD) = ANGLE(ED+60°+EGD)
@ TRIANGLES ARE SIMILAR IF THEY ARE THEIR ANGLES RESPECTIVELY EQUAL