Use triangle angle-side relationships and triangle inequality in mathematical and real-world problems.
Use the hinge theorem informally to compare third sides or included angles in two triangles
Problem
\(\text{Two}~\text{triangles}\) have \(\text{two}~\text{pairs}~\text{of}~\text{congruent}~\text{corresponding}~\text{sides}\), while their included angles measure \(50°\) and \(80°\). Apply the hinge theorem to identify the triangle with the longer side opposite its included angle and state the comparison principle.
The two congruent adjacent-side pairs make this a hinge comparison rather than a full congruence claim. We’ll confirm that the given angles are included between those sides, order the openings, and transfer that order to the third sides lying opposite them.
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