Concurrent line segments in a triangle

Median

Recall a line segment joining the vertex to the mid-point of the opposite side of a triangle.

In DABC, AD is the line segment drawn from A to BC (opposite side of A). AD is a median of a triangle.

"The line segment jointing a vertex of a triangle to the mid-point of the opposite is called a median of a triangle".

A triangle has 3 vertices and 3 sides. Hence, three medians can be drawn in a triangle.

Activity

Draw a triangle ABC. Mark the mid-points of BC, AC and AB as D, E and F respectively. Join AD, BE, CF.

AD, BE and CF are the three medians of DABC. They pass through (or meet) at the same point (or common point). G is the point of concurrence of the medians. It is called as centroid.

Centroid:

The medians of a triangle are concurrent. The point of concurrence of the medians of a triangle is called centroid. Centroid is denoted by G.

Altitude

Recall a perpendicular drawn from a vertex of a triangle to the opposite side of a triangle.

In DABC, AD is drawn perpendicular to BC. Draw a triangle PQR. Draw perpendiculars (altitudes) from P, Q and R to the opposite sides. The three altitudes meet at a point. Let this point be 'O'. O is the point of concurrence of the three altitudes of DPQR.

The altitudes of a triangle are concurrent. The point of concurrency of the altitudes is called orthocentre. It is denoted by 'O'.

In addition to the medians and altitudes as concurrent lines, we have the angle bisectors and perpendicular bisectors of the sides, which concur at a point.