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 deg.

Step-by-step explanation:

Given: ∠DEG ≅ ∠EFG ≅ 60°

To Prove : ΔDEF is similar to ΔDEG

Proof : ∠DEG ≅ ∠EFG ≅ 60°    [Given]

Let ∠ GEF = x°

Then ∠EGD = (60+x)°    Since exterior angle of a triangle is equal                to the sum of opposite interior angles.

Now in ΔDEF and ΔDEG attached in the figure,

∠DEF ≅ ∠EGD ≅ (60 + x)°

∠D is common in both the triangles.

∠EFD ≅ ∠DEG ≅ 60°

Hence  ΔDEF and ΔDEG are similar.            

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