Theorem 6.1 Concurrency of Altitudes of a Triangle The medians of a triangle intresect at a point that is two third of distance from each vertex to the midpoint of the opposite side.ĭefinition: An altitude of a triangle is a perpendicular segment from vertex to the opposite side or the line that contains the opposite side.ĭefinition: The point of concurrency of the altitudes called the orthocenter of the triangle. Theorem 5.1 Concurrency of Medians of a Triangle The centroid is always inside the triangle. The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.ĭefinition:A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.ĭefinition: The point of concurrency of the medians is called the centroid of the triangle. Theorem 4.1 Concurrency of Perpendicular Bisectors of a Triangle The perpendicular bisector of a triangle intersect at a point that is equidistant from the vertices of the triangle.ĭefinition: The point of concurrency of the angle bisectors is called the incentsr of the triangle and it always lies inside the triangle. Theorem 3.1 Concurrency of Perpendicular Bisectors of a Triangle The point of intersection of lines is called the point of concurrency.ĭefinition: The point of concurrency of the perpendicular bisectors of triangles is called the circumcenter of the triangle. If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle.ĭefinition:When three or more lines intersect in the same point, they are called concurrent lines. Theorem 2.2 Converse of the Angle Bisector Theorem If a point is on the bisector of an anlgle, then it is equidistant from the two sides of the angle. If DA = DB, then D lies on the perpendicular bisector of AB.ĭefinition: The distance from a point to a line is define as the length of the perpendicular segment from the point to the line.ĭefinition: When a pint is the same distance from one line as it is from another line, then the point is equidistant from the two lines. If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. Theorem 1.2 Converse of the Per pendicular Bisector Theorem If CP is the perpendicular bisector of AB, then CA = CB If a point is on perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Theorem 1.1 Perpendicular Bisector Theorem A segment, ray, line or palne that is perpemndicular to a segment at its midpoint is called a perpendicular bisector.
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