Question

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.

Answer 1

I hope this helps you

Answer 2

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.