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

	Created by liyana45 over 10 years ago

High School Diploma Math Note on Unit Three-Geometric Properties, created by liyana45 on 21/12/2013.