Question

Given: ΔDFE is isosceles with base FE; FB ≅ EC. Prove: ΔDFB ≅ ΔDEC 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

Answer 1

The answer is:

1. It is given

2. DE

3. DFE and DEF

4. DFB and DEC

Hope it helps!

Answer 2

Answer:

Step-by-step explanation:

Given: ΔDFE is isosceles with base FE; FB ≅ EC.

To prove: ΔDFB ≅ ΔDEC

Proof: It is given that  ΔDFE is isosceles with base FE; FB ≅ EC, thus

From ΔDFB and ΔDEC, we have

FB≅EC (Given)

DF≅DE (Definition of isosceles triangle)

∠DFE≅∠DEF⇒∠DFB≅DEC (because DF≅DE, therefore base angles are equal)

Thus, by SAS rule,

ΔDFB ≅ ΔDEC

Statements                                                           Reasons

1. FB≅EC                                                               (Given)

2. DF≅DE                                           (Definition of isosceles triangle)

3.∠DFE≅∠DEF

⇒∠DFB≅DEC            (because DF≅DE, therefore base angles are equal)

4. ΔDFB ≅ ΔDEC                                            SAS rule