1.Which of the following is true about the bisectors of a segment in a plane?
A) Every segment has exactly one bisector.
B) Every segment has exactly two bisectors.
C) Every segment has 10 bisectors.
D) Every segment has infinitely many bisectors.
Is the answer A?
Nevermind, is the answer D?
if you mean a line segment, and the bisectors are also to be line segments, then there are many bisectors, but they are all perpendicular to the segment, and they all go through the midpoint of the segment.
So, yes: D.
Ok, thank you so much.
No, the answer is not A) Every segment has exactly one bisector.
To determine the correct answer, let's discuss what a bisector of a segment is. A bisector of a segment is a line or line segment that divides the original segment into two equal parts. It can be imagined as a line or segment that passes through the midpoint of the original segment and forms two congruent segments.
Now, let's evaluate each option:
A) Every segment has exactly one bisector.
This statement is incorrect. A segment can have infinitely many bisectors, as any line or line segment passing through its midpoint would be a bisector. Therefore, option A is not true.
B) Every segment has exactly two bisectors.
This statement is also incorrect. As stated earlier, a segment can have infinitely many bisectors. Therefore, option B is not true.
C) Every segment has 10 bisectors.
This statement is not true either. A segment can have infinitely many bisectors, not just ten. Therefore, option C is not true.
D) Every segment has infinitely many bisectors.
This statement is correct. As mentioned earlier, any line or line segment passing through the midpoint of the segment will divide it into two congruent parts, making it a bisector. Since there are infinitely many lines or line segments that can pass through the midpoint, there are infinitely many bisectors. Therefore, option D is the correct answer.
So, the correct answer is D) Every segment has infinitely many bisectors.