1 Def: Median Def: A median of a triangle is a line segment that joins any vertex of the triangle to the midpoint of the opposite side. Every triangle has three medians. Examples: Median In each case below, make a congruence statement about 2 line segments. E F G H L P Q R S T V

Geometry Lesson: Median, Altitude, Angle Bisector Def: Altitude Def: An altitude of a triangle is a line segment drawn from any vertex of the triangle, perpendicular to and ending on the opposite side. Every triangle has three altitudes. Examples: Altitude In each case below, state the name of an altitude and the triangle to which it belongs. 1) B A D C L K P BN G 2) 3) A B C

Geometry Lesson: Median, Altitude, Angle Bisector Def: Angle Bisector Def: An angle bisector of a triangle is a line segment that bisects any angle of the triangle, and terminates on the side opposite the angle. Every triangle has three angle bisectors. Examples: Angle bisector ) ) ( ( ) ) P AQ D L X ( (

Geometry Lesson: Median, Altitude, Angle Bisector Ex: Special line segments of triangles P Q R T X 1) 2) T P X R Q 3) ( ( T X P R

5Geometry Lesson: Median, Altitude, Angle Bisector Proofs w/Median, Altitude, Angle Bisector What conclusions can we make based on medians, altitudes and angle bisectors of triangles? A B C D

6Geometry Lesson: Median, Altitude, Angle Bisector Proofs w/Median, Altitude, Angle Bisector T N X L 1) Given: Prove: 2) Given: Prove: 3) Given: Prove:

7Geometry Lesson: Median, Altitude, Angle Bisector Proofs w/Median, Altitude, Angle Bisector T N X L R S 4) Given: Prove: