# CONSTRUCTION OF MEDIAN  OF A TRIANGLE

## About "Construction of median of a triangle"

Construction of median of a triangle :

Even though students know what is median, many students do not know, how to construct median of a triangle.

Here we are going to see "How to construct median of a triangle"

## Construction of median of a triangle

To construct median of a triangle, we must need the following instruments.

1. Ruler

2. Compass

Let us see, how to construct median of a triangle through the following example.

Construct median to the side BC of the triangle ABC with AB = 6 cm, BC = 7 cm and AC = 5 cm.

Step 1 :

Draw triangle ABC using the given measurements.

Step 2 :

Construct the perpendicular bisector of the side BC to find midpoint E of BC.

Step 3 :

Now, join the vertex A and the mid point E of BC.

Now, AE is the median to the side BC of the triangle ABC.

This construction clearly shows how to draw median of a triangle with compass and straightedge or ruler. The median divides the side into two equal halves.

In the above example, median AE divides the side BC  in to two equal halves.

From the steps of construction of median of a triangle, first we have to know, how to construct perpendicular bisector.

So, let us see, how to construct perpendicular bisector.

## Construction of perpendicular bisector of a line segment

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. Since this bisects, it finds the midpoint of the given 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.

After having gone through the stuff given above, we hope that the students would have understood "Construction of median of a triangle"

If you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6