Altitudes of a Triangle An altitude is a line segment from a vertex of a triangle to the opposite side. It forms a triangle with the vertex and the two l...
An altitude is a line segment from a vertex of a triangle to the opposite side. It forms a triangle with the vertex and the two legs.
The altitudes of a triangle can be classified into two types:
Exterior altitudes: These altitudes extend outside the triangle.
Internal altitudes: These altitudes extend inside the triangle.
Exterior Altitudes:
The altitude from vertex A to side BC is the line segment AB.
The altitude from vertex A to side CD is the line segment AC.
The altitude from vertex A to side BC is the line segment AD.
Internal Altitudes:
The altitude from vertex A to side BC is the line segment AC.
The altitude from vertex A to side CD is the line segment BD.
The altitude from vertex A to side BC is the line segment AD.
The altitudes of a triangle play an important role in determining the area of the triangle. They help to divide the area of the triangle into smaller parts, which can be used to calculate the area.
Properties of Altitudes:
The altitude from a vertex to a side is perpendicular to the side.
The altitude from a vertex to a side divides the triangle into two equal parts.
The area of the triangle is equal to the product of the areas of the triangles formed by the altitudes from the three vertices