Date: Topic: Altitudes, Medians, and Bisectors ____ (6.4) Warm-up: *Don’t forget to mark your diagram!!

Altitudes An altitude of a triangle is a line segment through the ______ of an angle and is ________________ to the side opposite that angle. Each triangle has ________ altitudes. They intersect at a point called the _____________. Sometimes the orthocenter is outside of the triangle

Constructing a perpendicular line from a point to a line (or segment)

Constructing Altitudes

Medians The median of a triangle is a line segment joining a _________ of an angle to the ____________ of the side opposite that angle. Each triangle has ________ medians. They intersect at a point called the _________.

Constructing a midpoint

Constructing Medians

Bisectors A perpendicular bisector is a _____ ________ passing through the midpoint of the segment and forming a ___ _______ angle. The _______ perpendicular bisectors of a triangle intersect at a point, called the _____________. An angle bisector is a line segment through the ________ of an angle, creating two angles of _______ _____________. The _______ angle bisectors of a triangle intersect at a point, called the __________.

Constructing a perpendicular bisector

Constructing perpendicular bisectors Q P

Constructing an angle bisector Q

Constructing angle bisectors P Q R

Mid-segments A mid-segment is a line segment connecting the midpoints of ____ ________ of a triangle. The mid-segment of a triangle is equal to ______ of the third side. ? 14 The mid-segment and the third side are ___________. Example: Find x:

Example: is the perpendicular bisector of side Find and 3x + 5 4x - 6

Example: is the angle bisector of Find