Question

Complete the two-column proof using the answers in the bank. Given: DF ≅ EF FG bisects ∠DFE Prove: ∆DFG ≅∆EFG

Answer 1

Answer:

Reasons:

1. Given

2. Given

3. Definition of bisector

4. Reflexive property

5. SAS Congruence

Step-by-step explanation:

This is quite easy to solve. All that you're expected to do is to complete the reason that justifies each statement given in the two-column proof.

Let's complete the proof as follows:

1. Statement: $DF \cong EF$

1. Reason: Given

We know this statement is true because we are given in the question.

2. Statement: FG bisects <DFE

2. Reason: Given

We also know this because we are told so in the question, as shown in the diagram given.

3. Statement: $\angle 1 \cong \angle 2$

3. Reason: Definition of bisector

We know this because an angle bisector divides an angle into two equal halves. Therefore, the definition of bisector justifies why it was stated that $\angle 1 \cong \angle 2$

4. Statement: $\overline{FG} \cong \overline{FG}$

Reason: Reflexive property.

5. Statement: ∆DFG $\cong$ EFG

5. Reason: SAS Congruence

Two sides (DF and FG) and an included angle (angle 1) of ∆DFG is congruent two corresponding sides (EF and FG) and an included angle (angle 2) of ∆EFG. Therefore, ∆DFG $\cong$ EFG by the Side-Angle-Side (SAS) Congruence Theorem.