Category: Geometry

Points, Lines, and Circles Associated with a Triangle

Select your language EnglishSpanish Every triangle has lines (also called cevians) and points that determine a number of important elements. There are many different constructions that find a special point associated with a triangle,...

Perpendicular Bisector of a Triangle

Select your language EnglishSpanish The perpendicular bisector of a segment is a line perpendicular to the segment that passes through its midpoint. It has the property that each of its points is equidistant from...

Median of a triangle

Select your language EnglishSpanish The median of a triangle is a line segment that joins one of its vertices with the center of the opposite side. Every triangle has three medians (ma, mb and...

Triangle Center

Select your language EnglishSpanish Some classical triangle centers are: Centroid (G) Orthocenter (H) Circumcenter (O) Incenter (I) Centroid of a Triangle The centroid of a triangle (or barycenter of a triangle) G is the...

Altitude of a Triangle

Select your language EnglishSpanish The altitude of a triangle, or height, is a line from a vertex to the opposite side, that is perpendicular to that side. It can also be understood as the...

Angle bisector of a triangle

Select your language EnglishSpanish The angle bisector of a triangle is a line segment that bisects one of the vertex angles of a triangle, and ends up on the corresponding opposite side. There are...

Incenter of a triangle

Select your language EnglishSpanish The incenter of a triangle (I) is the point where the three interior angle bisectors (Ba, Bb y Bc) intersect. The angle bisector of a triangle is a line segment...

Circumcenter of a triangle

Select your language EnglishSpanish The circumcenter of a triangle (O) is the point where the three perpendicular bisectors (Ma, Mb y Mc) of the sides of the triangle intersect. It can be also defined...

Orthocenter of a triangle

Select your language EnglishSpanish In a triangle ABC the orthocenter H is the intersection point of the three altitudes of the triangle. Every triangle has three altitudes (or heights) and three sides (or bases)....

Centroid of a Triangle

Select your language EnglishSpanish The centroid of a triangle (or barycenter of a triangle) G is the point where the three medians of the triangle meet. The medians of a triangle are the line...