- Books Name
- CBSE Class 7 Mathematics Book

- Publication
- Param Publication

- Course
- CBSE Class 7

- Subject
- Mathmatics

**Medians of a Triangle and Centroid**

**Medians :-**

AB, BC, CA are the sides of and AD is a line segment which intersects side BC of at point D such that AD bisects the side BC. This line segment AD is called the median of .

A median is a line segment which connects a vertex of a triangle to the mid point of the opposite side.

**Centroid :-**

• Centroid is the point of intersection of all three medians of a triangle.

• In the given figure G is the centroid of

• A centroid of a triangle cuts the median in the ratio 2 : 1

*⟹* AG : GD = 2 : 1

- Books Name
- class 7 Mathematics Book

- Publication
- ReginaTagebücher

- Course
- CBSE Class 7

- Subject
- Mathmatics

**Altitude of a triangle**

An altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex).

In ∆ ABC, AD is the altitude of triangle ABC.

Through each vertex, an altitude can be drawn. So, there are at most three altitudes in a triangle.

Properties of Altitudes of a Triangle

- Every triangle has 3 altitudes, one from each vertex. AE, BF and CD are the 3 altitudes of the triangle ABC.
- The altitude is the shortest distance from the vertex to its opposite side.
- The 3 altitudes always meet at a single point, no matter what the shape of the triangle is.
- The point where the 3 altitudes meet is called the ortho-centre of the triangle. Point O is the ortho-centre of the triangle ABC.
- The altitude of a triangle may lie inside or outside the triangle.