Question

problem 17: (first taught in lesson 49) from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: ∠dfe > ∠def prove: de > df

Explanation:

Step1: Recall triangle side - angle relationship

In a triangle, the larger angle is opposite the longer side.

Step2: Identify angles and sides

In \(\triangle DFE\), \(\angle DFE\) is opposite side \(DE\) and \(\angle DEF\) is opposite side \(DF\).

Step3: Apply the theorem

Since \(\angle DFE>\angle DEF\), by the theorem that in a triangle the larger angle is opposite the longer side, we can conclude \(DE > DF\).

Answer:

The theorem that in a triangle the larger angle is opposite the longer side.