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