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 ΔABC.
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 ΔABC.
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 ΔABC.
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
ΔABC 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 ΔABC is its
circumcircle.
