### Mathematics Class X

Real Numbers
Polynomials
Arithmetic Progressions
Triangles
Coordinate Geometry
Introduction to Trigonometry
Circles
Constructions
Areas Related to Circles
Surface Areas and Volumes
Statistics
Probability

# Centers of the Triangle

There are four different centers of the Triangle

1. Centroid of a Triangle

The point of intersection of the medians of the three sides of the Triangle is the centroid of that Triangle. It will always inside the Triangle.

1. Incenter of a Triangle

The point of intersection of the angle bisectors of the three angles of the Triangle is called the incenter of that Triangle. It is the point from where the circle is inscribed in the Triangle.

1. Circumcenter of the Triangle

The point of intersection of the perpendicular bisectors of the three vertices of the Triangle is called the circumcenter of that Triangle . It is not always inside the Triangle. It could be outside the Triangle for obtuse Triangle and fall at the midpoint of the hypotenuse of the right angled Triangle.

1. Orthocenter

The point of intersection of the altitudes of the Triangle is the orthocenter of that Triangle.  Also falls outside the Triangle in case of obtuse Triangle and it falls at the vertex of the Triangle in case of right angle Triangle.

Similarity Criteria of Two Polygons Having the Same Number of Sides

Any two polygons which have the same number of sides are similar if the following two criteria are met-

1. Their corresponding angles are equal, and
2. Their corresponding sides are in the same ratio (or proportion)
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