LESSON 5-3 MEDIANS, ALTITUDES & ANGLE BISECTORS OF TRIANGLES OBJECTIVE: To define and use medians, altitudes and angle bisectors of triangles
DEFINITIONS: is a segment whose endpoints are A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.
A B C EX. #1 Sketch, label and mark 3 medians for ABC. E F D
An altitude of a triangle is a segment from a vertex of the triangle and perpendicular to the line containing the opposite side.
EX. #2 Sketch, label & mark altitudes for each of the 3 triangles. A D B E C F T Y Q R S X U T V Z
An angle bisector in a triangle is a segment that bisects one of the angles of a triangle and whose endpoints are on the triangle.
C EX. #3 Sketch, label and mark angle bisectors for CAR. B O X A R
Complete the following proof: Given: AB CB BD is a median of ABC Given: AB CB BD is a median of ABC Prove: ABD CBD D A B C
1. BD is a med of ABC 1. GIVEN 2. D is the midpt of AC STATEMENTS REASONS 1. BD is a med of ABC 1. GIVEN 2. D is the midpt of AC 2. Def. of med. 3. AD CD 3. Def. of midp. 4. AB CB 4. GIVEN
5. BD BD 5. Ref. Prop 6. SSS Post. 6. ABD CBD 7. CPCTC
ASSIGNMENT: Lesson 5.3 Worksheet