Question

(c) problem 16: (first taught in lesson 44)
from this given statement, select the definition, property,
postulate, or theorem that justifies the prove statement.
given: $overrightarrow{pd}-overrightarrow{pe}-overrightarrow{pf}$;
prove: $mangle dpf>mangle epf$

Explanation:

Step1: Recall angle - related theorems

The Exterior - Angle Inequality Theorem states that the measure of an exterior angle of a triangle is greater than the measure of either of the non - adjacent interior angles.

Step2: Analyze the given angles

In the context of angles with a common vertex \(P\), \(\angle DPF\) can be considered as an 'exterior' type angle (in a non - triangle sense, but in terms of the relative position of rays) with respect to \(\angle EPF\). Since \(\overrightarrow{PD}\), \(\overrightarrow{PE}\), and \(\overrightarrow{PF}\) are given such that \(\overrightarrow{PD}\) is 'outside' relative to \(\overrightarrow{PE}\) and \(\overrightarrow{PF}\) in the angular sense, the measure of \(\angle DPF\) is greater than the measure of \(\angle EPF\), which is justified by the Exterior - Angle Inequality Theorem.

Answer:

The Exterior - Angle Inequality Theorem.