Aim: Do Now: Ans: 5 5 miles 4 miles Ans: 3 miles P A B C What is the median, altitude and angle bisector of a triangle? Aim: Do Now: 1) What is the median of the numbers –4, -1, 0, 5, 6, 8, 10 ? Ans: 5 2) What is the altitude in miles of the plane in the diagram? 5 miles 4 miles Ans: 3 miles P A B C Geometry Lesson: Median, Altitude, Angle Bisector

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. Def: Median Examples: Median • • • In each case below , make a congruence statement about 2 line segments. P Q R S T V E F G H L

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. Def: Altitude Examples: Altitude In each case below, state the name of an altitude and the triangle to which it belongs. 3) A B C 1) B A D C L K P B N G 2) Geometry Lesson: Median, Altitude, 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. Def: Angle Bisector Examples: Angle bisector ) ) ( P A Q D L X ( Geometry Lesson: Median, Altitude, Angle Bisector

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

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

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