LESSON 5-3 MEDIANS, ALTITUDES & ANGLE BISECTORS OF TRIANGLES

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Presentation transcript:

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