How To Identify Segment Bisector

A perpendicular bisector can be defined as a line that intersects another line segment perpendicularly and divides it into 2 parts of equal measurement. Nosotros can draw a perpendicular bisector using a rule, a compass and a pencil.

Two lines are said to exist perpendicular to each other when they intersect each other at xc degrees or at correct angles. And, a bisector is a line that divides a line into two equal halves. Thus, a perpendicular bisector of a line segment AB implies that it intersects AB at ninety degrees and cuts it into ii equal halves.

What is a Perpendicular Bisector?

A perpendicular bisector is a line that bisects another line segment at a right bending, through the intersection point. Thus, we tin can say, a perpendicular bisector always divides a line segment through its midpoint. The term bifurcate itself means dividing every bit or uniformly.

Backdrop of a Perpendicular Bisector

It divides AB into two equal halves or bisects it.
It makes right angles with (or is perpendicular to) AB.
Every signal in the perpendicular bisector is equidistant from point A and B.

While working with applied geometry, y'all will oft find the application of perpendicular bisectors; say when you are asked to depict an isosceles triangle, or when you have to make up one's mind the middle of a circle, etc. Below are the steps to construct a perpendicular bisector of a line using a compass and a ruler.

How to Construct a Perpendicular Bisector?

You will require a ruler and compasses. The steps for the construction of a perpendicular bisector of a line segment are:

Step 1: Draw a line segment PQ.
Step ii: Adjust the compass with a length of a little more than half of the length of PQ.
Step 3: Place the compass pointer at betoken P and draw arcs above and below the line.

Construction of perpendicular bisector- 1

Step four: Keeping the same length in the compass, place the compass pointer at point Q. Similarly, draw 2 arcs above and beneath the line keeping the compass pointer at Q.

Construction of perpendicular bisector- 2

Step v: Mark the points where the opposite arcs cantankerous every bit Ten and Y.

Construction of perpendicular bisector 3

Step half dozen: Using a ruler, depict a line passing across X and Y.

Construction of perpendicular bisector 4

The perpendicular bisector bisects PQ at a indicate J, that is, the length PJ is equal to JQ. And the angle between the two lines is 90 degrees.

Perpendicular Bisector of Triangles

The perpendicular bisector of a triangle is the line segment that is fatigued from a vertex to the contrary side bisecting the side at a right bending. The perpendicular of a triangle is perpendicular to the sides drawn from the opposite vertices and divides the sides into ii equal parts. The point at which all the iii perpendicular bisectors of a triangle meets is called the circumcenter of a triangle.

Perpendicular bisector of triangle

Solved Examples

Q.ane: If a line segment is of length equal to 8cm and a perpendicular bisector is drawn to it. What is the mensurate of each part of the line segment?

Solution: By the definition, we know, a perpendicular bisector intersects a line segment at the right angle and divides it into two equal parts.

Hence, the measure of each part of the line segment (8 cm), which is bisected past a perpendicular is 4 cm.

Q.ii: Tin we depict a perpendicular bisector, if the length of the radius of a circumvolve is known?

Solution: Yes, we can describe the perpendicular bisector if nosotros know the radius of the circle. Since the bore of a circle is equal to twice of radius. Hence. we tin draw a perpendicular bisector to the diameter of circumvolve following the aforementioned steps.

Practice Questions

Draw a perpendicular bisector to a line segment equal to 12 cm.
Construct a perpendicular bisector of a line segment equal to 6.6 cm.

Frequently Asked Questions on Perpendicular Bisector

What does a Perpendicular Bisector Hateful?

A perpendicular bisector can be defined every bit a line segment which bisects some other line segment at 90 degrees. In other words, a perpendicular bisector intersects another line segment at ninety° and divides it into two equal parts.

Tin a Perpendicular Bisector be a Median of a Triangle?

Yes, a perpendicular bisector can be a median of a triangle. A median is defined equally a line segment from a vertex of a triangle to the midpoint of the side opposite that vertex. And then, if the median joins the contrary side at 90 degrees, it volition be the perpendicular bisector of that side. For example, for an equilateral triangle, the medians are always perpendicular bisectors.

What is the Point at Which the Perpendicular Bisectors of a Triangle Meet Called?

The point at which the perpendicular bisectors of a triangle encounter are known every bit the circumcenter of the triangle and it is equidistant from all the vertices.

What is Perpendicular Bisector Theorem?

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.