3. Exterior angles of a triangle

ALTITUDES OF A TRIANGLE AND ORTHOCENTRE

AD is a line segment which is perpendicular to the side BC of ∆ABC .This line segment AD is called as altitude of ∆

Altitude is also called as height of a triangle. In the given figure AD is the height of ∆ ABC  from vertex A to side BC.

•    Orthocentre is the meeting point of all three altitudes of a triangle.
•    In the given figure H is the orthocentre of ∆ ABC.
•    In obtuse-angled triangle the orthocentre lies outside the triangle.
•    In Acute-angled triangle the orthocentre lies inside the triangle.
•    In a Right-angled triangle, the right angle lies at the vertex at which the right angle is formed.

Exterior angles of a triangle

An exterior angle of a triangle is equal to the sum of the opposite interior angles.   

In the above figure, ∠ACD is the exterior angle of the Δ ABC.
So, ∠ACD = ∠CAB + ∠CBA
At each vertex of a triangle, an exterior angle of the triangle may be formed by extending one side of the triangle.