Question

given △dfe is isosceles with base fe,
prove: △dfb ≅ △dec
complete the missing parts of the paragraph proof.
we know that triangle dfe is isosceles with base fe and that segment pb is congruent to segment ec because
segment df is congruent to segment △ by the definition of isosceles triangle. since these
segments are congruent, the base angles angles
△ and △ are congruent by the isosceles triangle theorem. therefore, triangles
△ and △ are congruent by sas

Explanation:

Step1: Identify congruent segments

Since \(\triangle DFE\) is isosceles with base \(FE\), by the definition of isosceles triangle, segment \(DF\) is congruent to segment \(DE\).

Step2: Identify congruent angles

Given \(PB\cong EC\), and because \(\triangle DFE\) is isosceles, the base angles \(\angle DCE\) and \(\angle DBF\) are congruent by the isosceles triangle theorem.

Answer:

First blank: \(DE\); Second blank: \(DCE\) and \(DBF\)