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Question

# The Hinge Theorem is also known as the Side-Angle-Side Inequality Theorem or SAS Inequality Theorem. How are the requirements for applying the Hinge Theorem similar to the requirements for applying SAS? How are the requirements different?

Solution

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The requirements are similar in a sense that we must be given two corresponding sides and their included angles before applying the respective theorems.

The requirements are different in a sense that the two corresponding sides must be congruent and the included angle be congruent for SAS Theorem but the included angles for the Hinge Theorem are not necessarily congruent. In SAS Theorem, we determine the congruence the two triangles while for the Hinge Theorem, the two triangles' third sides are being compared.

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