Terms Related to Triangles Conditions

# Terms Related to Triangles Conditions

## Triangle

A triangle is a closed plane figure bounded by three straight line segments. There are three vertices, three sides and three angles in a triangle.

In the given figure, ABC is a triangle.

Its sides are AB, BC and AC.
Three angles are ABC, BCA and CAB.
The vertices are A, B and C.

## Interior and Exterior Angles

The three angles enclosed within the triangle at each vertex are known as interior angles.
The angle between a side of the triangle and the extension of an adjacent side is known as the exterior angle.

In the given figure, 1, 2, 3 are the interior angles and 4, 5, 6 are the exterior angles.

# Important Terms Related to Triangles

## Median

A median of a triangle is the line segment joining any of its vertices to the mid-point of the opposite side. There are three medians in a triangle.
In the following figure, AD is the median and D is the mid-point of BC.

## Centroid

A centroid is the point at which all the three medians of a triangle intersect each other. In the given figure, O is the centroid of Î”ABC.

## Altitude

An altitude is the perpendicular drawn from any vertex to the opposite side. There are also three attitudes in a triangle, which need not lie inside the triangle. In the given figure, AD is the altitude of Î”ABC.

## Orthocenter

An orthocenter is the point at which all the three altitudes of a triangle intersect each other. In the given figure, X is the orthocenter of Î”ABC.

## Incenter

The point of intersection of the internal angle bisectors of a triangle is its incenter. In the given figure, O is the point of intersection of the angle bisectors AD, BE and CF.

## Incircle

Incircle of a triangle is the circle whose center is the incenter and which touches all the three sides of the triangle. In the given figure, the circle inscribed inside Î”ABC is its incircle.

## Circumcenter

The point of intersection of all the three perpendicular bisectors of a triangle is known as circumcenter. In the given figure, O is the circumcenter.

## Circumcircle

Circumcircle is the circle whose center is the circumcenter and which passes through all the vertices of the triangle. In the given figure, the circle outside Î”ABC is its circumcircle.