Perpendicular Bisector in a Triangle

In geometry, the perpendicular bisector of a side in a triangle is a line that divides that side into two equal segments and is perpendicular to it. When the perpendicular bisectors of all three sides of a triangle are extended, they intersect at a single point known as the circumcenter. The circumcenter is a significant point in a triangle because it is equidistant from all three vertices of the triangle.

This property of the circumcenter depict that it is the center of the unique circle that can be drawn to circumscribe or pass through all three vertices of the triangle. This circle is called the circumcircle. The circumcircle with the circumcenter as its center, touches each vertex of the triangle making it important in geometry and trigonometry.

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Perpendicular Bisector

Perpendicular Bisectors are the lines that bisect the other line at right angles. Perpendicular bisectors are a fundamental building block in Euclidean geometry. The perpendicular bisector divides a line into two halves and is equidistant from the endpoints. The concept of a perpendicular bisector is fundamental for constructing various geometric shapes and solving problems involving lines and segments. Perpendicular bisectors are often represented as a dashed line with a right angle symbol to indicate their perpendicular nature.

In this article, we will discuss what is perpendicular bisector, the equation for a perpendicular bisector, the construction of a perpendicular bisector, and the perpendicular bisector theorem in detail.

Table of Content

  • What is a Perpendicular Bisector?
  • Equation for a Perpendicular Bisector
  • How to Draw a Perpendicular Bisector?
  • Perpendicular Bisector Theorem
  • Construction of a Perpendicular Bisector
  • Perpendicular bisector in a Triangle

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What is a Perpendicular Bisector?

Perpendicular bisector is a geometric construction that guarantees a line, ray, or line segment intersects another line segment at a right angle while also dividing it into two halves. It plays a vital role in geometry, trigonometry, and engineering serving as a basis for various geometric proofs and calculations. A perpendicular bisector divides another line segment into two equal parts while forming a right angle (90 degrees) with it. We can consider a perpendicular bisector to cut the original line in half and always perpendicular to the original line....

Equation for a Perpendicular Bisector

The equation for a perpendicular bisector involves several steps....

How to Draw a Perpendicular Bisector?

Below are the steps to drawing a perpendicular bisector:...

Perpendicular Bisector Theorem

Perpendicular Bisector Theorem states that if a point lies on the perpendicular bisector of a line segment then it is equidistant from the endpoints of the segment. In other words, the distance from the point to each endpoint is the same....

Construction of a Perpendicular Bisector

Construction of perpendicular bisector is simple. To construct a perpendicular bisector, you can locate the midpoint of the line segment. Then, use a compass to draw two equal circles with their centers at the endpoints of the segment. Where the circles intersect is the intersection point of the perpendicular bisector....

Perpendicular Bisector Line Segment

‘Perpendicular bisector line segment’ refers to a line segment that is drawn perpendicular to another line segment and intersects it at the midpoint. The perpendicular bisector divides the original segment into two congruent parts ensuring equal distances to the segment’s endpoints....

How do You Find the Perpendicular Bisector?

To find the perpendicular bisector of a line segment, calculate the midpoint of the segment, and then determine the negative reciprocal of the original segment’s slope. With the midpoint and the slope, you can write the equation of the perpendicular bisector. To calculate a perpendicular bisector, you can follow below steps:...

Perpendicular Bisector in a Triangle

In geometry, the perpendicular bisector of a side in a triangle is a line that divides that side into two equal segments and is perpendicular to it. When the perpendicular bisectors of all three sides of a triangle are extended, they intersect at a single point known as the circumcenter. The circumcenter is a significant point in a triangle because it is equidistant from all three vertices of the triangle....

Solved Examples on Perpendicular Bisector

Example 1. Draw a 6 cm line and construct a perpendicular bisector on it....

Practice Problems on Perpendicular Bisector

Q1. Draw a 5 cm line and construct a perpendicular bisector on it....

Perpendicular Bisector – FAQs

1. What is a Perpendicular Bisector?...