Question
Which properties are true for all perpendicular bisectors? Choose all that apply.(3 points)%0D%0AResponses%0D%0A%0D%0ACut an angle into half%0D%0ACut an angle into half%0D%0A%0D%0ACut a segment in half%0D%0ACut a segment in half%0D%0A%0D%0AForm a 90 degree angle with a segment%0D%0AForm a 90 degree angle with a segment%0D%0A%0D%0ASplit a segment in two equal segments
Answers
GPT-4o mini
The properties that are true for all perpendicular bisectors are:
1. **Cut a segment in half** - A perpendicular bisector will intersect a segment at its midpoint, effectively dividing it into two equal parts.
2. **Form a 90 degree angle with a segment** - A perpendicular bisector by definition creates a 90-degree angle with the segment it bisects.
3. **Split a segment in two equal segments** - This is essentially the same as "cut a segment in half". When a perpendicular bisector cuts a segment, it splits that segment into two equal segments.
The statement "Cut an angle into half" is not true for perpendicular bisectors; that would be true for angle bisectors instead.
So the correct options are:
- Cut a segment in half
- Form a 90 degree angle with a segment
- Split a segment in two equal segments
1. **Cut a segment in half** - A perpendicular bisector will intersect a segment at its midpoint, effectively dividing it into two equal parts.
2. **Form a 90 degree angle with a segment** - A perpendicular bisector by definition creates a 90-degree angle with the segment it bisects.
3. **Split a segment in two equal segments** - This is essentially the same as "cut a segment in half". When a perpendicular bisector cuts a segment, it splits that segment into two equal segments.
The statement "Cut an angle into half" is not true for perpendicular bisectors; that would be true for angle bisectors instead.
So the correct options are:
- Cut a segment in half
- Form a 90 degree angle with a segment
- Split a segment in two equal segments