Question

which theorem would explain why pq > sr?
converse of hinge theorem
hinge theorem
pythagorean theorem
triangle inequality theorem

Explanation:

The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, the triangle with the larger included angle has the longer third side. Here, sides SP ≅ SR and SQ is common (congruent to itself) in triangles SPQ and SRQ. The included angle at S for triangle SPQ is 48°, which is larger than the included angle 46° for triangle SRQ. Thus, the third side PQ (opposite 48°) is longer than SR (opposite 46°), matching the Hinge Theorem.

Answer:

Hinge Theorem