MID-TERM STUFF HONORS GEOMETRY

Theorem Polygon Angle Sum Theorem The sum of the measures of the angles in a polygon is (n – 2)180. Find the sum of the measure of the angles of a 15-gon.

Theorem: Polygon Angle-Sum Theorem The sum of one set of exterior angles for any polygon is 360°. 1 5 2 4 3 m<1 + m<2 + m<3 + m<4 + m<5 = 360°

Definitions Concurrent lines: three or more lines intersect in the same point. Point of concurrency: the point of intersection of the lines.

Definition of a Median A median is a segment from a vertex of a triangle to the midpoint of its opposite side.

Definition of a Centroid The centroid is the point of concurrency of the medians.

THEOREM

How does CM related to HC? Find HC =

Altitude An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side.

PERPENDICULAR BISECTORS A perpendicular bisector of a triangle: It is a line (ray or segment) that is perpendicular to the side of a triangle at its midpoint.

Isosceles Triangle Vertex Angle Leg Leg Base Angle Base Base Angle Base angles of an Isosceles triangle are congruent & the legs of an Isosceles Triangle are congruent

The bisector of the vertex angle of an isosceles triangle is the median, altitude & perpendicular bisector. midpoint.