Which of the following best describes a perpendicular bisector of a segment?

A perpendicular bisector is a line that bisects a line segment in two equal parts and makes an angle of 90 degrees at the point of intersection. In other words, we can say that a perpendicular bisector divides a line segment at its midpoint making an angle of 90 degrees.

A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of (left figure). The perpendicular bisector of a line segment can be constructed using a compass by drawing circles centered at and with radius and connecting their two intersections.

The bisector is a line that divides a line or an angle into two equivalent parts. The bisector of a segment always contains the midpoint of the segment.

Is the perpendicular bisector always the midpoint?

Perpendicular Bisector of a Triangle

The perpendicular bisector of the sides of the triangle is perpendicular at the midpoint of the sides of the triangle. The point at which all the three perpendicular bisectors meet is called the circumcenter of the triangle.

Which of the following is a perpendicular bisector theorem?

The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints. In other words, if we hanged laundry lines from any floor of our tower, each floor would use the same length of laundry line to reach the ground.

Answer. Perpendicular bisector is a straight line or a segment that passes through the midpoint of a line that cuts the segment into 2 equal parts at 90 degrees.

What are formed when a perpendicular bisector is present in a triangle?

The three perpendicular bisectors of the sides of a triangle meet in a single point, called the circumcenter . A point where three or more lines intersect is called a point of concurrency. So, the circumcenter is the point of concurrency of perpendicular bisectors of a triangle. Here, O is the circumcenter of ΔXYZ .

What is true about all of the points that are on the perpendicular bisector of a segment?

Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. In addition to the Perpendicular Bisector Theorem, we also know that its converse is true.

Is the perpendicular bisector of a segment equidistant from the endpoints of that segment?

A segment, ray, line, or plane that is perpendicular to a segment at its midpoint is called a perpendicular bisector. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Point is equidistant from two points if its distance from each point is the same.

Does a perpendicular bisector of a triangle always pass through the opposite vertex?

Additionally, the fact that a given line is a perpendicular bisector of one side of a triangle, and passes through the opposite vertex, is proof that the triangle is isosceles. This triangle was formed by connecting a point on the perpendicular bisector to both endpoints of the original segment.

A median is defined as a line segment from a vertex of a triangle to the midpoint of the side opposite that vertex. So, if the median joins the opposite side at 90 degrees, it will be the perpendicular bisector of that side. For example, for an equilateral triangle, the medians are always perpendicular bisectors.

Which of the following statements is the converse of perpendicular bisector theorem?

The converse of the perpendicular bisector theorem states that if a point is equidistant from both the endpoints of the line segment in the same plane, then that point is on the perpendicular bisector of the line segment.

It can be concluded then that all three perpendicular bisectors, FD, FE, and FG, are concurrent at point F because point F is equidistant from all three vertices of the triangle. This point is also called the circumcenter because it is the center of the circle that circumscribes the triangle.

Perpendicular bisector theorem deals with congruent segments of a triangle, thus allowing for the diagonals from the vertices to the circumcenter to be congruent. Whereas the angle bisector theorem deals with congruent angles, hence creating equal distances from the incenter to the side of the triangle.

Segment bisector is a line, ray, or segment that cuts another line segment at the center dividing the line into two equal halves. The line always bisects or passes through the midpoint of the line segment dividing it into two equal parts.