Question

given: △dfe is isosceles with base fe; fb ≅ ec. prove: △dfb ≅ △dec complete the missing parts of the paragraph proof. we know that triangle dfe is isosceles with base fe and that segment fb 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, are congruent by the isosceles triangle theorem. therefore, triangles are congruent by sas.

Explanation:

Step1: Identify given information

It is given in the problem statement.

Step2: Recall isosceles - triangle property

In an isosceles triangle $\triangle DFE$ with base $\overline{FE}$, the non - base sides are congruent, so $\overline{DF}\cong\overline{DE}$.

Step3: Recall isosceles - triangle theorem

The base angles of an isosceles triangle are congruent. For isosceles $\triangle DFE$, $\angle DFB\cong\angle DEC$.

Step4: Apply SAS congruence

We have $\overline{FB}\cong\overline{EC}$, $\angle DFB\cong\angle DEC$, and $\overline{DF}\cong\overline{DE}$, so $\triangle DFB\cong\triangle DEC$ by SAS (Side - Angle - Side) congruence criterion.

Answer:

1. Given
2. $\overline{DE}$
3. $\angle DFB$ and $\angle DEC$
4. $\triangle DFB$ and $\triangle DEC$