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 legs of isosceles △DFE

△DFE is isosceles with base FE, so legs DF ≅ DE (def. of isosceles △).

Step2: Identify base angles of △DFE

Base angles of isosceles △ are congruent, so ∠DFB ≅ ∠DEC (base ∠s of isosceles △).

Step3: Use given congruent segments

Given FB ≅ EC.

Step4: Apply SAS congruence rule

△DFB ≅ △DEC by SAS (DF≅DE, ∠DFB≅∠DEC, FB≅EC).

Answer:

△DFB ≅ △DEC