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More About Triangles Medians Is a segment in a triangle that joins a vertex of the triangle and the midpoint of the side opposite that vertex The medians of a triangle intersect at a common point called the centroid. When three or more lines or segments meet at the same point, they are concurrent. The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint. Altitudes and Perpendicular Bisectors A perpendicular segment in which one endpoint is at a vertex and the other endpoint is on the side opposite that vertex. A segment or line that contains the midpoint of the side of a triangle and is perpendicular to that side. Angle Bisectors of Triangles A ray whose endpoint is the vertex and is located in the interior of the angle that separates a given angle into two angles with equal measure Isosceles Triangles If two sides of a triangle are congruent, then the angles opposite those sides are congruent. The median from the vertex angle of an isosceles triangle lies on the perpendicular bisector of the base and the angle bisector of the vertex angle. If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Right Triangles The side opposite the right angle The two sides that form the right angle If two legs of one right triangle are congruent to the corresponding legs of another right triangle then the triangles are congruent. The Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the lengths of the legs a and b. Distance on the Coordinate Plane If d is the distance between two points (x1, y1) and (x2, y2), then d = (x2 – x1 + (y2 – y1 2 ) 2 )