In this section, you will learn how to construct perpendicular bisector of a line segment.

**Key Concept - Perpendicular Bisector**

The line drawn perpendicular through the midpoint of a given line segment is called the perpendicular bisector of the line segment.

To construct a perpendicular bisector of a line segment, you must need the following instruments.

1. Ruler

2. Compass

The steps for the construction of a perpendicular bisector of a line segment are :

**Step 1 :**

Draw the line segment AB.

**Step 2 :**

With the two end points A and B of the line segment as centers and more than half the length of the line segment as radius draw arcs to intersect on both sides of the line segment at C and D.

**Step 3 :**

Join C and D to get the perpendicular bisector of the given line segment AB.

In the above figure, CD is the perpendicular bisector of the line segment AB.

This construction clearly shows how to draw the perpendicular bisector of a given line segment with compass and straightedge or ruler.

This bisects the line segment (That is, dividing it into two equal parts) and also perpendicular to it.

The perpendicular bisector of a triangle is a line which is passing through the mid point of the side and also perpendicular to that side.

**Step 1 :**

Draw the triangle ABC.

**Step 2 :**

Select one the sides of the triangle, say AC

With the two end points A and C of the side AC as centers and more than half the length of the side AC as radius draw arcs to intersect on both sides of the side AC and join the points of intersection of the arcs.

Using the steps explained above, in the above triangle ABC, perpendicular bisector is drawn to the side AC.

Similarly we can draw perpendicular bisectors to the sides AB and BC as given below.

So, every triangle will have three perpendicular bisectors.

**Key Concept - C****ircumcenter**

The point of concurrency of the perpendicular bisectors of the three sides of a triangle is called the circumcenter and is usually denoted by S.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**