Which of the following statements are true? Choose all that apply.
(1 point) only two choices
Responses
The perpendicular bisector of a segment is equidistant from the endpoints of that segment.
The perpendicular bisector of a segment is equidistant from the endpoints of that segment.
A perpendicular bisector can intersect the segment it bisects at any point.
A perpendicular bisector can intersect the segment it bisects at any point.
An angle bisector is equidistant from the sides of the angle it is bisecting.
An angle bisector is equidistant from the sides of the angle it is bisecting.
An angle bisector creates two congruent vertical angles.
The following statements are true:
1. The perpendicular bisector of a segment is equidistant from the endpoints of that segment.
2. A perpendicular bisector can intersect the segment it bisects at any point.
3. An angle bisector is equidistant from the sides of the angle it is bisecting.
The statement about an angle bisector creating two congruent vertical angles is false. An angle bisector creates two congruent angles, but they are not necessarily vertical angles.
These are the two correct answers
The perpendicular bisector of a segment is equidistant from the endpoints of that segment.
An angle bisector is equidistant from the sides of the angle it is bisecting.
Apologies for the error in my previous response. You are correct, the two statements that are true are:
1. The perpendicular bisector of a segment is equidistant from the endpoints of that segment.
2. An angle bisector is equidistant from the sides of the angle it is bisecting.
Thank you for pointing out the mistake.
The statements that are true are:
1. The perpendicular bisector of a segment is equidistant from the endpoints of that segment.
Explanation: A perpendicular bisector is a line that bisects a given segment into two equal parts and is perpendicular to that segment. As a result, it will always be equidistant from the endpoints of the segment.
2. An angle bisector is equidistant from the sides of the angle it is bisecting.
Explanation: An angle bisector is a line or ray that divides an angle into two equal angles. It will always be equidistant from the sides of the angle it is bisecting.
Therefore, the statements (1) and (3) are true.
To determine which of the statements are true, we will analyze each statement individually:
1. The perpendicular bisector of a segment is equidistant from the endpoints of that segment.
This statement is true. The perpendicular bisector of a segment is a line that divides the segment into two equal parts at a 90-degree angle. By definition, it is equidistant from the endpoints of the segment.
2. A perpendicular bisector can intersect the segment it bisects at any point.
This statement is true. A perpendicular bisector can intersect the segment it bisects at any point along its length. As long as the line meets the criteria of bisecting the segment and being perpendicular to it, it can intersect at any location.
3. An angle bisector is equidistant from the sides of the angle it is bisecting.
This statement is false. An angle bisector divides an angle into two equal angles. While the angle bisector does pass through the vertex of the angle, it is not necessarily equidistant from the sides of the angle. The distance from the angle bisector to the sides of the angle depends on the specific measurements of the angle.
4. An angle bisector creates two congruent vertical angles.
This statement is false. An angle bisector creates two congruent angles, but they are not necessarily vertical angles. Vertical angles are formed by the intersection of two lines, and an angle bisector divides an angle into two smaller angles.
Therefore, the true statements are:
- The perpendicular bisector of a segment is equidistant from the endpoints of that segment.
- A perpendicular bisector can intersect the segment it bisects at any point.