Question

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.

Answer 1

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