Question

Given Line segment E D is-congruent-to Line segment D B , which statements about the figure are true? Check all that apply.

Line segment E B is bisected by Line segment D F .

A is the midpoint of Line segment F C .

Line segment F C bisects Line segment D B.

Line segment E B is a segment bisector.

FA = One-halfFC.

Line segment D A is congruent to Line segment A B .

Answer 1

1, 2, 4, 5

Explanation:

Line segment E B is bisected by Line segment D F .

A is the midpoint of Line segment F C .

Line segment E B is a segment bisector.

FA = One-halfFC.

Answer 2

A, B, D and E.

Explanation:

From the diagram

`ED \cong DB\\FA \cong AC`

• Since D is the midpoint of EB, Line segment EB is bisected by Line segment DF.
• Since
  `FA \cong AC`, A is the midpoint of Line segment FC.
• EB bisects FC at point A, therefore, Line segment E B is a segment bisector.

• Point A divides FC into two equal parts, FA and AC, therefore
  `FA=(1)/(2)FC`

The correct options are A, B, D and E.