1. 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

2. 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

3. 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

4. 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

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

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

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