Remember what each result states and look at the common parts. You can see a difference by looking at their conclusions.
One similarity is that both results involve two pairs of congruent sides and its included angle. The difference between them is that, in the Hinge Theorem, the included angles are not congruent, whereas in the SAS Postulate they are.
Practice makes perfect
Let's remember what the Hinge Theorem states.
Hinge Theorem
If two sides of a triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.
One similarity we can see is that both results involve two pairs of congruent sides and its included angle. The difference between them is that, in the Hinge Theorem, the included angles are not congruent, whereas in the SAS Postulate they are.
We can also say that the Hinge Theorem concludes a side inequality or an angle inequality, while the SAS Postulate concludes a triangle congruence.
