Perpendicular Bisector – Definition & Properties


Do you know what the term “bisect ”means? The term bisect in simple words means to divide or split a line into two. A perpendicular bisector makes a right angle to the baseline and splits a given line segment into two equal-length halves. The phrase ‘bisect’ refers to splitting evenly. Perpendicular bisectors cross the line segment they bisect and form four 90° angles on opposite sides. A perpendicular line or line segment is one that forms a 90° angle with another line or line segment.

In this article, we are going to know more about perpendicular bisectors and perpendicular lines in detail.

Properties of Perpendicular Bisector

Let’s go through the properties of a perpendicular bisector –

  • A line segment or a line is divided into two congruent segments
  • Divides a triangle’s sides into congruent sections.
  • They form a 90° angle with the line being bisected.
  • They meet in the halfway line segment.
  • A triangle’s circumcenter is the point at which its perpendicular bisectors connect.
  • They meet within a triangle in an acute triangle, outside a triangle in an obtuse triangle, and at the hypotenuse in a right triangle.
  • Any location on the perpendicular bisector is equidistant from both ends of the segment bisected.
  • For a given line segment, there can only be one.

What is Perpendicular Bisector Theorem?

A line segment’s perpendicular is defined as a line that splits another line segment in half at 90o via its midpoint. According to the perpendicular bisector theorem, any point on the perpendicular bisector is equidistant from both endpoints of the line segment on which it is drawn. If a pillar is positioned at an angle in the center of a bridge, all of its points will be equidistant from the bridge’s endpoints.

The perpendicular bisector is a line segment that divides a line into equal-sized segments by crossing it perpendicularly. When two lines intersect in such a way that they form a 90-degree angle with one another, they are said to be perpendicular to one another. In contrast, a bisector divides a line into equal halves(two).

What are Perpendicular Lines?

Joseph was starving and craved a sandwich. His sandwich was usually sliced into four equal pieces by his mother. Sometimes it’s across the center, and other times it’s from corner to corner. In any case, a perpendicular line was sliced across the sandwich.

A perpendicular line is one that intersects another at a 90° angle. Each corner forms a 90° angle with the others. This is also referred to as a right angle.

So, where do we look for perpendicular lines? They are, after all, everywhere. They can be found in nature and are employed in geometry. Even perpendicular angles can be found at the corners of squares and possibly triangles. Let’s look at some instances!

Definition of Perpendicular Lines

Perpendicular lines are two different lines that cross at a 90° angle. Have you spotted anything like the letter “L” or the connecting corners of your walls? They are perpendicular lines, which are straight lines that meet at a specified angle – the right angle.

A line is known to be perpendicular to another line if the two meet at a 90° angle. Let’s take a closer look at the notion of perpendicular lines.

If you want to understand the topic in a fun way, you can visit the Cuemath website.

Do perpendicular lines have the same slope?

The slopes of perpendicular lines are not the same. Perpendicular line slopes differ from one another in a certain way. The slope of one line is equal to the inverse of the slope of the other line. The sum of a number and its reciprocal equals 1.

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