Exercise 42 Page 446

From the expression △ A B C ≅ △ E D F, we can identify corresponding vertices. A &→ E B &→ D C &→ F With this information we can mark the corresponding angles in our congruent triangles.

As we can see, △ DGB has two congruent angles. Therefore, by the Converse of the Base Angles Theorem we can claim that △ DGB is an isosceles triangle.

Let's show this as a two-column proof.

Statement	Reason
1. △ ABC ≅ △ EDF	1. Given
2. ∠ B ≅ ∠ D	2. ≅ Δ → ≅ parts
3. GD≅ GB	3. Converse of the Base Angles Theorem
4. △ DBG is isosceles	4. Definition of an isosceles triangle