Question

which of the following statements must be true based on the diagram below? select all that apply. (diagram is not to scale.)
answer attempt 3 out of 5
$overline{ec}$ is a segment bisector.
$overline{ec}$ is a perpendicular bisector.
$overline{ec}$ is an angle bisector.
$e$ is the vertex of a right angle.
$c$ is the vertex of a right angle.
none of the above.

Explanation:

1. $\overline{EC}$ is a segment bisector: The tick marks show $DE = EB$, so $\overline{EC}$ splits $\overline{DB}$ into two equal parts, making this true.
2. $\overline{EC}$ is a perpendicular bisector: A perpendicular bisector must be perpendicular to the segment and bisect it. $\overline{EC} \perp \overline{DB}$ (right angle mark) and bisects $\overline{DB}$, so this is true.
3. $\overline{EC}$ is an angle bisector: There are no marks showing $\angle DCE = \angle BCE$, so this cannot be confirmed.
4. $E$ is the vertex of a right angle: The right angle symbol at $E$ confirms $\angle DEC$ (and $\angle BEC$) is a right angle, so this is true.
5. $C$ is the vertex of a right angle: There is no right angle mark at $C$, so this is false.

Answer:

$\overline{EC}$ is a segment bisector.
$\overline{EC}$ is a perpendicular bisector.
$E$ is the vertex of a right angle.