Question

A conjecture and the paragraph proof used to prove the conjecture are shown.

Given: E is the midpoint of segment D F. Prove: 2 D E equals D F. A segment DF is horizontal with endpoints D and F. E is the midpoint of the segment.



Drag an expression or statement to each box to complete the proof.

Answer 1

1. DF (option 3)

2. segment addition postulate

3. segment congruence postulate

4. DF (option 5)

Answer 2

Answer with explanation:

Given: E is the mid point of DF.

Prove: 2 DE=D F

Proof with explanation:

It is given that
`\Bar{DE}` is mid point of
`\Bar{DF}`.

1.→

So,
`\Bar{DE}\cong\Bar{DF}`

-------------------------By Definition of mid point

2.→ DE=E F----------------Segment Congruence Postulate

3.→DE+E F=D F ----------------Segment Addition Postulate

4.→DE+DE=D F-------------By Substitution

5.→Simplifying gives

2 DE=D F