# Altitude and Median of triangle

In this chapter, we will learn important different between median and altitude of triangle with examples.

## Difference between altitude and median

(a) Definition of Altitude and median

Median Definition
The line segment joining the vertex and mid point of opposite side of triangle is called median.

Altitude Definition
The line segment joining the vertex and opposite side at 90 degree angle is called an altitude of triangle.

In the above triangle ABC, AM is the altitude and BN is the median.

Since AM is the altitude, \mathtt{\angle AMB\ =\ 90\ degree}

Since, AN is the median, BN = NC.

(b) Location of median and altitude.

The median of triangle always lie inside the triangle, while the altitude of triangle can be located inside or outside the triangle.

For example, consider the below obtuse triangle, here the median is located inside while the altitude is located outside the triangle.

Here the median is AM since it divide the side BC into two equal parts.

The altitude is AN, since it intersect the other side in perpendicular degree.

(c) Division of triangle

The median divides the triangle into two equal parts while the altitude doesn’t divide it into equal parts.

(d) Number of altitude and median

All the triangles have exactly three medians and altitudes.

(e) Intersection of medians and altitudes

The point of intersection of three medians is called centroid of triangle. Centroid is also a point around which the triangle’s mass is equally distributed.

The centroid is very important concept for physics related problems.

The point of intersection of three altitudes is called orthocenter of triangle.

(f) Location of centroid and orthocenter

The centroid is always located inside the triangle.

The location of orthocenter can be inside or outside the triangle depending on the type of triangle.

If the figure is acute triangle then the orthocenter will lie inside the triangle.

In obtuse triangle, the orthocenter is located outside the triangle.

Given above is the obtuse triangle with orthocenter O outside the triangle.

(g) Coinciding altitude and median

In equilateral triangle, both altitude and median are the same line.

Consider the above equilateral triangle ABC. Here the segment AM is both altitude and median of triangle.

Since AM is the altitude; \mathtt{\angle AMC\ =\ 90\ degree}

As AM is also the median, it means the vertex BC is divided into equal parts.

i.e. BM = MC.