Question

from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: parallelogram stvw and ( mangle stp>mangle tsp ) prove: ( sp > tp ) a b c d e if unequal sides, then unequal angles

Explanation:

Step1: Recall the triangle - side - angle relationship

In a triangle, if \(m\angle A>m\angle B\), then the side opposite \(\angle A\) is longer than the side opposite \(\angle B\).
In \(\triangle STP\), \(\angle STP\) and \(\angle TSP\) are angles, and \(SP\) is the side opposite \(\angle STP\), \(TP\) is the side opposite \(\angle TSP\).

Step2: Apply the relationship

Since \(m\angle STP > m\angle TSP\) in \(\triangle STP\), by the theorem "If Unequal Angles, then Unequal Sides" (the converse of the "If Unequal Sides, then Unequal Angles" theorem), the side opposite the larger angle is longer.

Answer:

The theorem that justifies \(SP > TP\) is the "If Unequal Angles, then Unequal Sides" theorem.