Unit Three-Geometric Properties

Unit Three Key Concepts -the medians of a triangle meet at a single point, the centroid. - each median bisects the area of the triangle. - the median from the vertex between the equal sides of an isosceles triangle is the same as the altitude to the vertex and bisects the angle at the vertex -The centroid of a triangle divides each median into two parts, with one part twice the length of the other - the altitude is a perpendicular line from each vertex CENTROID   ORTHOCENTER 1: Find equation of line perpendicular to one side. 2: Plug in opposite vertex coordinate. 3: Do same for one more line, then use substitution/elimination to find POI.   CIRCUMCENTER 1: Find equation of perpendicular bisector of one of the lines (midpoint, perp. Slope of line) 2: Repeat for one more line. 3: Find POI using substitution or elimination - the line segment joining the midpoints of two sides of a triangle is parallel to the third side, and half its length -the diagonals of a parallelogram bisect each other -joining the midpoints of the adjacent sides of any quadrilateral forms a parallelogram - the line segment joining the midpoints of the non-parallel sides of a trapezoid is parallel to the parallel sides and has a lenth equal to the mean of the lengths of the parallel sides - the diameters of a circle intersect at the centre of the circle - the right bisector of a chord of a circle passes through the centre of the circle. - the right bisectors of two chords of a circle intersect at the centre of the circle. -there is only one circle that passes through three given non-collinear points

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