If two sides of a triangle are congruent to two sides of another triangles, and the third side in the first is longer than the third side in the second triangle, then the included angle in the first triangle has a greater measure than the included angle in the second triangle.
Now, let's copy the diagram and mark the angles we are asked to compare.
We can make some observations about the sides of the two triangles by using the fact that segments of equal length are congruent. Notice that two sides of △ ABC are congruent to two sides of △ DEG.
AC&≅GD
CB&≅DE
However, the third side of △ ABC is longer than the third side of △ DEG. Therefore, by the Converse of the Hinge Theorem, the included angle measure in △ ABC is greater than the included angle measure in △ DEG.
BA> EG
⇓
m∠ ACB> m∠ GDE
