Aim:

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

2. Def: Median • • • F G P Q L R H E S T V 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.

3. Def: Altitude 3) B 1) 2) A P K L G A C C B D N B 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. Geometry Lesson: Median, Altitude, Angle Bisector

4. Def: Angle Bisector ) ) ) ( ) ( P ( ( D L X A Q 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 Geometry Lesson: Median, Altitude, Angle Bisector

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

6. B C D A 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

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

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