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The point at which all the altitudes of a  triangle intersect. In an acute triangle the orthocenter is in the middle of the triangle, in an obtuse triangle the orthocenter is the outside of a triangle, while in a right triangle the orthocenter is on the triangle.This is an acute triangle therefore the orthocenter is in the center.

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A line that extends from the vertex of a triangle to form a right triangle.AD is an altitude of triangle ABC

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The centroid theorem states that the distance between the centroid and the vertex is 2/3 the distance between the vertex of the triangle and the midpoint of the opposite side

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The centroid of a triangle is the point at which all medians meet in a triangle. The centroid is always in the center of the triangle .The centroid in this image is G.

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A median in a triangle is a line drawn from one vertex of an angle to the midpoint of the opposite line. The median shown in this draving is AD

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The incenter is the point where all angle bisectors of a triangle meet. This point is always on the inside of a triangle.This is a drawing of the incenter of the triangle

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A segment that divides an angle into two equal angles.

This is an image of an angle bisector. The angle is RPQ and the bisector is PL.

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The point at where all perpendicular bisectors meet is called the circumcenter. The circumcenter can be either inside on, or outside the triangle. The circumcenter theorem states that the circumcenter of a triangle are equidistant from the vertices

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A perpendicular bisector is a  segment that bisects a segment  into two different right angles. The perpendicular bisector in the image is KN