Subscribe to our YouTube channel for the latest videos, updates, and tips.


Construction of Perpendicular Bisector

Here we will learn how to construct a perpendicular bisector of a line segment.

The perpendicular bisector of a line segment is the line that is perpendicular to the line segment at its mid-point.

In the adjoining Fig., \(\overleftrightarrow{PO}\) is the perpendicular bisector of \(\overline{AB}\) bisecting \(\overline{AB}\) at O i.e., \(\overline{AO}\) = \(\overline{BO}\)

First Method: To Draw the Perpendicular Bisector with the Help of Transparent Tapes

Working Rules To Draw the Perpendicular Bisector:

Step I: Draw a line segment PQ.

Perpendicular Bisector with the Help of Transparent Tapes


Step II: Paste a strip of a transparent rectangular taps diagonally across the end-points P and Q as shown in the figure.

Step III: Repeat the process as in step-2 by placing another taps over P and Q just diagonally across the previous one. Thus, two strips cross at M and N.

Construction of Perpendicular Bisector

Step IV: Join M and N to get \(\overline{MN}\) and \(\overline{PQ}\) as the required perpendicular bisectors of each other.


Second Method: To Draw the Perpendicular Bisector using Ruler and Compasses

Working Rules To Draw the Perpendicular Bisector:

Step I: Draw a line segment AB of any length.

Draw a Line Segment AB


Step II:
Using compass, draw an arc with A as centre and a radius more than half the length of \(\overline{AB}\)

Draw Line Segment AB


Step III:
With B as a centre and same radius as in step-II, draw another arc to intersect the previous arc at P and Q.

Rules to Draw the Perpendicular Bisector


Step III: Join P and Q to get \(\overleftrightarrow{PQ}\). It cuts AB at O. This line PQ bisects the given line segment AB at O. i.e. \(\overline{AO}\) = \(\overline{BO}\)

Draw the Perpendicular Bisector


What would happen?

In steps II and III above, what would happen, if we take less than half of the length as radius and draw arcs?


Solved Examples on Construction of Perpendicular Bisector:

1. Draw a line segment AB of length 8 cm. Using compass, divide it into four equal parts.

Solution:

Step I: Draw a line segment AB = 8 cm and draw a perpendicular bisector using steps given in the Working Rules.

Examples on Construction of Perpendicular Bisector

Step II: In step I, we have divided \(\overline{AB}\) into two equal parts \(\overline{AC}\) and \(\overline{BC}\) Similarly, draw the perpendicular bisectors of \(\overline{AC}\) and overline BC separately. 

Solved Examples on Construction of Perpendicular Bisector

Now, we obtain four equal parts of \(\overline{AB}\)

i.e., \(\overline{AD}\) = \(\overline{CD}\) = \(\overline{CE}\) = \(\overline{BE}\) = 2 cm .


Worksheet on Construction of Perpendicular Bisector:

1. Draw a line segment of 8.5 cm and draw its perpendicular bisector.

2. Divide a line segment of length 8 cm into four equal parts using compass.

3. Draw a circle of radius 5 cm. Draw two chords on it. Constrct the perpendicular bisector of these chords. Where do they meet?

4. Draw a triangle. Construct three perpendicular bisectors on each of its side. Check whether all three bisectors meet at one point.

5. Divide a line segment of length 10 cm into four equal parts using compass.



5th Grade Geometry

5th Grade Math Problems

From CConstruction of Perpendicular Bisector of a Line Segment to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Speed Distance and Time | Relation between Speed Distance and Time

    May 21, 25 12:58 PM

    Speed is defined as the distance covered per unit time. Speed = (Distance Travelled)/(Time Taken) Or, S = D/T. Speed also requires a unit of measurement. If the distance is in kilometres

    Read More

  2. Math Problem Answers | Solved Math Questions and Answers | Free Math

    May 21, 25 12:45 PM

    Partial fraction
    Math problem answers are solved here step-by-step to keep the explanation clear to the students. In Math-Only-Math you'll find abundant selection of all types of math questions for all the grades

    Read More

  3. Test of Divisibility | Divisibility Rules| Divisible by 2, 3, 5, 9, 10

    May 21, 25 10:29 AM

    The test of divisibility by a number ‘x’ is a short-cut method to detect whether a particular number ‘y’ is divisible by the number ‘x’ or not. Test of divisibility by 2: A number is divisible by 2

    Read More

  4. Divisible by 7 | Test of Divisibility by 7 |Rules of Divisibility by 7

    May 21, 25 10:17 AM

    Divisible by 7
    Divisible by 7 is discussed below: We need to double the last digit of the number and then subtract it from the remaining number. If the result is divisible by 7, then the original number will also be

    Read More

  5. Average Word Problems | Worksheet on Average Questions with Answers

    May 20, 25 05:40 PM

    In average word problems we will solve different types of problems on basic concept of average. 1. Richard scored 80, 53, 19, 77, 29 and 96 runs in 6 innings in a series. Find the average runs scored…

    Read More