1. Line Segments Associated with Triangles Ch. 5-1
Geometry
St. Barnabas HS
Bronx, NY

2. 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

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

4. Definition: 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.
Altitudes:
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)

5. Defintion: 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.
Angle bisectors: ) ) ( P A Q D L X (
Geometry Lesson: Median, Altitude, Angle Bisector

6. 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

7. In ABC, AM is median to BC. If AB = 16, AC = 7, and BC = 11, find BM.
BM  MC
= 5.5 B
BM + MC = BC = 11 B M N C A
In the same ABC, BM = 3x – 2 and CM = x Find the value of x and BC
3x – 2 = x + 8
2x – 2 =
2x =
x =
BC = BM + CM = (3x – 2) + (x + 8)
= (3·5 – 2) + (5 + 8)
= (13) + (13) = 26

8. 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

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

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