A perpendicular bisector can be defined as a line that intersects another line segment perpendicularly and divides it into two parts of equal measurement. We can draw a perpendicular bisector using a rule, a compass and a pencil. Show
Two lines are said to be perpendicular to each other when they intersect each other at 90 degrees or at right 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 90 degrees and cuts it into two equal halves. What is a Perpendicular Bisector?A perpendicular bisector is a line that bisects another line segment at a right angle, through the intersection point. Thus, we can say, a perpendicular bisector always divides a line segment through its midpoint. The term bisect itself means dividing equally or uniformly. Properties of a Perpendicular Bisector
While working with practical geometry, you will often find the application of perpendicular bisectors; say when you are asked to draw an isosceles triangle, or when you have to determine the centre 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:
The perpendicular bisector bisects PQ at a point J, that is, the length PJ is equal to JQ. And the angle between the two lines is 90 degrees. Perpendicular Bisector of TrianglesThe perpendicular bisector of a triangle is the line segment that is drawn from a vertex to the opposite side bisecting the side at a right angle. The perpendicular of a triangle is perpendicular to the sides drawn from the opposite vertices and divides the sides into two equal parts. The point at which all the three perpendicular bisectors of a triangle meets is called the circumcenter of a triangle. Related ArticlesPerpendicular LinesConstruction of Perpendicular Line Through a PointConstruction Of Perpendicular LinesAngle Between Two LinesBisectorAngle Bisectors Solved ExamplesQ.1: If a line segment is of length equal to 8cm and a perpendicular bisector is drawn to it. What is the measure 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 by a perpendicular is 4 cm. Q.2: Can we draw a perpendicular bisector, if the length of the radius of a circle is known? Solution: Yes, we can draw the perpendicular bisector if we know the radius of the circle. Since the diameter of a circle is equal to twice of radius. Hence. we can draw a perpendicular bisector to the diameter of circle following the same steps. Practice Questions
Frequently Asked Questions on Perpendicular BisectorA perpendicular bisector can be defined as a line segment which bisects another line segment at 90 degrees. In other words, a perpendicular bisector intersects another line segment at 90° and divides it into two equal parts. Yes, a perpendicular bisector can be a median of a triangle. 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. The point at which the perpendicular bisectors of a triangle meet are known as the circumcenter of the triangle and it is equidistant from all the vertices. 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. |