Use triangle angle-side relationships and triangle inequality in mathematical and real-world problems.
Use side-angle relationships to compare routes or supports
Problem
\(\text{Two}~\text{triangular}~\text{braces}\) share \(\text{two}~\text{equal}~\text{side}~\text{lengths}\), but \(\text{one}~\text{brace}\) has a larger included angle. Use the side-angle relationship to compare the sides opposite those included angles.
The matched side pairs hold two parts of each brace fixed, leaving the included angle to control the endpoint separation. We’ll verify that hinge setup, identify the angle between the fixed sides, compare the openings, and use the Hinge Theorem to order the opposite spans.
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