Unit Three-Geometric Properties

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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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