# Altitudes of a Triangle

## Definition

• Altitude of the triangle: The perpendicular line segment from a vertex of a triangle to its opposite side is called an altitude of the triangle.
• Orthocentre: The altitudes of a triangle pass through exactly one point; that means they are concurrent. The point of concurrence is called the orthocentre.

## Notes

### Altitudes of the triangle:

• The perpendicular line segment from a vertex of a triangle to its opposite side is called an altitude of the triangle.

• An altitude has one endpoint at a vertex of the triangle and the other on the line containing the opposite side. Through each vertex, an altitude can be drawn.

• This line segment AD is an altitude of the triangle.

• A triangle has 3 altitudes.

#### The location of the orthocentre of a triangle:

The altitudes of a triangle pass through exactly one point; that means they are concurrent. The point of concurrence is called the orthocentre and it is denoted by ‘O’.

### Orthocentre of a triangle

Right angle triangle The legs of the triangle are two of the altitudes. The orthocenter is the vertex of the right angle.
Obtuse angled triangle

The orthocentre of an abtuse angled triangle is in the exterior of the triangle.

Acute angled triangle The orthocentre of an acute-angled triangle is in the interior of the triangle.
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