Triangle:  We just studied polygons. Triangle is a polygon with three sides. So, we could define a triangle as a plane closed figure bounded by three line segments.

A triangle is a polygon with three edges and three vertices. It is one of the most basic shapes in geometry. A triangle with vertices A, B, and C is denoted by ∆ABC.

Kind of Triangles

Classification of triangles based on the length of the sides

Scalene Triangle A triangle in which all three sides are of different lengths is called Scalene Triangle.

 

In this type of triangle:

\angle A \neq \angle B \neq \angle C

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Isosceles Triangle A triangle in which two sides are of the same length is called Isosceles Triangle

In this type of triangle:

\angle B = \angle C

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Equilateral Triangle A triangle in which all three sides are of the same length is called Equilateral Triangle.

 

In this type of triangle:

\angle A = \angle B = \angle C

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Some of the diagrams have been adopted from https://en.wikipedia.org/wiki/Triangle

Classification of Triangles based on the angles

Acute-angled Triangle A triangle in which all the three angles are more than0^{\circ} and less than 90^{\circ}  is called acute-angled triangle. t5
Right-angles Triangle A triangle in which one of the angles is 90^{\circ} is called right-angled triangle. t6
Obtuse-angled triangle A triangle in which one of the angles is more than 90^{\circ}  but less than 180^{\circ} is called obtuse-angled triangle. t7

Some of the diagrams have been adopted from https://en.wikipedia.org/wiki/Triangle

Term related to a Triangle

Median A line segment joining the vertex to the mid-point of the opposite side of a triangle is called median.

In this vertex

A  is meeting at point D (such that BD=DC ) midpoint of BC

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Centroid The point of intersection of three medians is called centroid.  

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Altitude The perpendicular drawn from the vertex to the opposite side.

Here AD   is the altitude of the triangle AD \ and\  BC is the base.

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Orthocenter The intersection of the three altitudes is called the Orthocenter of the triangle.

Here A is the Orthocenter of the triangle.

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Angle Bisector A line segment that bisects and interior angle of a triangle is called angle bisector.

Here AD is bisecting \angle BAC into two equal \angle BAD \ and\ \angle DAC

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Incentre and Incircle The point of intersection of internal angle bisectors is called the Incentre.

I is the Incentre of the triangle.

Now if you draw a circle with the center

I  in such a way that it touches all the three sides of the triangle, then that is called Incircle.

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Perpendicular Bisector or Right Bisector A line bisecting any side of the triangle and perpendicular to it is called perpendicular bisector of that side of the triangle.

Here BC is being bisected by DE. BD=DC \ and\ ED\perp BC.

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Circumcenter  and Circumcircle The point of intersection of the perpendicular bisectors of the sides of the triangle is called Circumcenter.

Here O   is the circumcenter.

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Exterior Angle and Interior Opposite Angles of a Triangle \angle ACD is the exterior angle and\angle CBA  and\angle BAC   are opposite interior angles of this exterior angle. t16

Some of the diagrams have been adopted from https://en.wikipedia.org/wiki/Triangle