Which of the following must be true about a perpendicular bisector and the segment it bisects? a. the perpendicular bisector and the segment bisect each other b. the angle of intersection depends on the length of the line segment c. the perpendicular bisector intersects the segment at a 45 degree angle.**** d. The perpendicular bisector intersects the segment at a 90 degree angle.
(d) is correct
that is, after all, what perpendicular means...
yes the correct answer is d. it says 'the perpendicular bisector intersects the segment at 90 degrees
The correct answer is c. the perpendicular bisector intersects the segment at a 45 degree angle.
To determine which statement is true about a perpendicular bisector and the segment it bisects, we need to understand the definition and properties of a perpendicular bisector.
A perpendicular bisector is a line that intersects a segment at its midpoint and forms a right angle (90 degrees) with that segment.
Now, let's analyze each statement:
a. "The perpendicular bisector and the segment bisect each other": This statement is not true. The perpendicular bisector bisects the segment into two equal parts, but the segment itself does not bisect the perpendicular bisector.
b. "The angle of intersection depends on the length of the line segment": This statement is not true either. The angle of intersection between the perpendicular bisector and the segment is always 90 degrees, regardless of the length of the line segment.
c. "The perpendicular bisector intersects the segment at a 45-degree angle": This statement is not true. As mentioned earlier, the perpendicular bisector always intersects the segment at a 90-degree angle, irrespective of its length.
d. "The perpendicular bisector intersects the segment at a 90-degree angle": This statement is true. The perpendicular bisector intersects the segment at a right angle, which is always 90 degrees.
Therefore, the correct answer is d. The perpendicular bisector intersects the segment at a 90-degree angle.