Question

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

Please explain the anwser, because I don't know how to do this correctly.

Answer 1

Reasons:

1. Given

2. Given

3. Definition of bisector

4. Reflexive property

5. SAS Congruence

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.