Question

point p is the incenter of \\( \triangle abc \\). which of the following segments are congruent to \\( \overline{pd} \\)? select all that apply.
\\( \overline{pe} \\)
\\( \overline{pf} \\)
\\( \overline{pb} \\)
\\( \overline{db} \\)
\\( \overline{cf} \\)

Explanation:

Step1: Recall the property of incenter

The in - center of a triangle is equidistant from the sides of the triangle. Point \(P\) is the in - center of \(\triangle ABC\). \(PD\perp AB\), \(PE\perp BC\), and \(PF\perp AC\).

Step2: Apply the equidistant property

Since the in - center is equidistant from the sides of the triangle, we have \(PD = PE=PF\) (the lengths of the perpendiculars from the in - center to the sides of the triangle are equal).

Answer:

\(\overline{PE}\), \(\overline{PF}\)