Medians and Altitudes of a Triangle A median is a line segment drawn from a vertex to the opposite side, opposite the angle at that vertex. There are thr...
A median is a line segment drawn from a vertex to the opposite side, opposite the angle at that vertex. There are three medians in a triangle: the median from vertex A, the median from vertex B, and the median from vertex C.
The altitude of a triangle is a line segment drawn from the vertex to the base, opposite the angle at that vertex. There are three altitudes in a triangle: the altitude from vertex A, the altitude from vertex B, and the altitude from vertex C.
The median theorem states that the three medians of a triangle intersect at a single point called the center of mass or centroid. The centroid divides each median into its two equal parts.
Examples:
In a triangle with vertices A, B, and C, the median from vertex A is segment AC, and the medians from vertices B and C are segments BC and DC, respectively.
In a triangle with angles measuring 45°, 60°, and 75°, the altitudes from vertices A, B, and C intersect at a point on the base, forming the angles 45°, 60°, and 75° at that point.
In a triangle with angles measuring 30°, 60°, and 90°, the medians from vertices A, B, and C intersect at a point on the base, forming the angles 30°, 60°, and 90° at that point