How Many Medians and Altitudes can the Triangle Have

Introduction

The median draws from the vertex of the triangle to the midpoint of the base of any triangle on the other side. Altitude draws from any vertex to the opposite side of the side, which is perpendicular to it. The number of medians and altitudes in a triangle counts three for both.

Median

Any triangle has 3 medians from its vertices, and there are some properties of a median in a triangle.

• The three medians of any triangle meet at a common point, which is known as the centroid of a triangle.

• So each median divides the triangle into two parts, and the area of the two parts of the triangle is the same.

• It means that these medians divide a triangle into six small equal triangles.

The median of the isosceles triangle is perpendicular to the base of a triangle.

The altitude of a triangle

An altitude is a point that starts from the vertex of a triangle and stretches to the opposite side of a triangle, forming a right angle on the opposite side.

Features of altitude of a triangle

• Any triangle also has three altitudes.

• The point where all three altitudes meet is called the orthocenter of any triangle.

• Thus, all these medians and altitudes meet at the center of a triangle.

• It is also the shortest distance between the vertex of a triangle to its base.

Can both median and altitude for a triangle be the same?

A median connects the midpoint of a triangle with the vertex, while the altitude connects the vertex of a triangle to the opposite side of the vertex, which forms the right angle.

Yes, it can be possible that one altitude and median can be the same if the triangle is isosceles, but with the equilateral triangle, all three medians are altitudes.

The altitude and median of the right-angle triangle and scalene triangle are not the same for any of the sides.

Are the altitudes of a triangle equal?

If all three sides of a triangle are the same, then all three altitudes are the same. Two altitudes are the same if the two sides of a triangle are the same. If all three sides are unequal, then the altitude of the triangle is also unequal.

Geometrical property of median

All three medians of a triangle are concurrent because they have a common intersection point. It divides each median with a ratio of 2:1, and we know this point as the centroid of a triangle.

Conclusion

We can conclude that it drew the median from the vertex to the midpoint of the opposite side, whereas it drew an altitude from the vertex of the triangle to the opposite side, being perpendicular to it.