This is because the perpendicular line drawn from the vertex of the triangle to the base cuts it equally. In an equilateral triangle, both the median and the altitude are the same. The number of altitudes and median a triangle could have is three for both. While altitude is drawn from any vertex of the triangle to the opposite side, perpendicular to it. The Median is drawn from the vertex of the triangle to the midpoint of the base. Although the only difference students can notice about median and altitude is the way it is drawn. The altitude and median of a triangle can be the same in many cases. By drawing the line segment with the midpoint, the base is already divided into equal sizes. And this is the way you make a median of a triangle. To the point formed by the intersection of arcs, draw a perpendicular line segment towards the base of the triangle.

First, you have to take a measurement on the compass and draw arcs with the same measurement towards the top from each side. In this method, what students must have is a scale, pencil and a compass. Thus, the triangle is Scalene with three different anglesĬonstructing the Median of A Triangle Using Compassĭrawing the median of a triangle by using a compass has a very easy method. We know that sum of all angles of a triangle = 180° The given angles of a triangle PQR are in the ratio of 3 : 2 : 1. However, in the case of an equilateral triangle, the median and altitude are always the same. Hence, a median needs not to be perpendicular every time. The altitude and median are not the same in a triangle.Īn altitude is a perpendicular bisector on any side of a triangle and it measures the distance between the vertex and the line which is the opposite side whereas, a median is a line segment that connects a vertex to the central point of the opposite side. If you’re confused between both these terms medians and altitudes of a triangle and you think whether they are the same or not then let me make it clear for you here. We can also see in the above diagram that the altitude is the shortest distance from the vertex to its opposite side.ĭifference Between Median and Altitude of a Triangle Just like median, we also have an attitude for triangle properties.Įvery triangle can have 3 altitudes i.e., one from each vertex as you can clearly see in the image below.Īll the 3 altitudes of a triangle always meet at a single point regardless of the shape of the triangle. However, we could do this from any vertex, but we most commonly see it from the top. In our triangle here in the above diagram, if we draw a line from vertex A perpendicular to the opposite side, it will be known as an altitude. These six (6) triangles formed by three (3) medians also consist of equal areas.Īn altitude is basically a perpendicular line segment that is drawn from a vertex of a triangle to the opposite side. In fact, the two new triangles formed by adding a median have equal areas. And this single point is known as the Centroid of the triangle. However, when we draw three medians, they always meet at a single point. In a triangle, we can have up to three medians, one from each vertex. We hope the available content will help you understand the chapter medians and altitudes of triangles in a better way.

Let’s learn about two more terms “altitude and median of the triangle” in the following article. So, in the below diagram line “AB” is called a “Median”. That means we know that it's a median if we have got those equal line segments. It splits the opposite side of the triangle into two equal line segments. A Median of a triangle is a straight line segment which is drawn from the vertex of a triangle to the middle point of the opposite side.

Efine altitude geometry