Question

Point B is the midpoint of .

Which statements about the figure must be true? Select three options.

DBC is bisected by ray BD.
ABC is bisected by ray BD.
BC = AC

2mDBC = mABC

Answer 1

point b is the midpoint of AC and ABC is bisected by ray BD.

Answer 2

Options B, C and D are correct choices.

Explanation:

We have been given a diagram in which point B is the midpoint of line ABC. We are asked to choose the correct statements about our given diagram.

A. DBC is bisected by ray BD.

Since DBC is an angle for our given diagram and side BD is terminal side of angle DBC, therefore, option A is false.

B. ABC is bisected by ray BD.

We have been given that point B is the midpoint of segment ABC, this means that ray BD bisect line ABC. Therefore, option B is true.

C.
`BC=(1)/(2)*AC`

Since point B is midpoint of line ABC, so AB will be equal to BC.

`AC=AB+BC`

`AC=BC+BC`

`AC=2BC`

`(AC)/(2)=(2BC)/(2)`

`(AC)/(2)=BC`

Therefore, option C is the correct choice.

D.
`2m\angle DBC=mABC`

We can see that measure of angle DBC is 90 degrees. We can see that ABC is a line and measure of linear angle is 180 degrees, therefore,
`2m\angle DBC=mABC` and option D is true.