define perpendicular Bisector.
Answers
Answer:
A perpendicular bisector can be defined as a line segment which intersects another line perpendicularly and divides it into two equal parts. Two lines are said to be perpendicular to each other when they intersect in such a way that they form 90 degrees with each other. And, a bisector 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.
Properties 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 point in the perpendicular bisector is equidistant from point A and B.
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.
Frequently Asked Questions
What does a Perpendicular Bisector Mean?
A 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.
Can a Perpendicular Bisector be a Median of a Triangle?
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 to 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.
What is the Point at Which the Perpendicular Bisectors of a Triangle Meet Called?
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.
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.
a perpendicular is drawn on the given line AB which bisects it in two equal parts at the 90⁰ angle so this perpendicular is known as perpendicular bisector.....
