1. 3.4 Beyond CPCTC Objective:
After studying this lesson you will be able to identify medians and altitudes of triangles. Understand why auxiliary lines are used in some proofs. Write proofs involving steps beyond CPCTC.

2. A O C D T G
Definition: A median of a triangle is a line segment drawn from any vertex of the triangle to the midpoint of the opposite side. (A median divides into two congruent segments, or bisects the side to which it is drawn.)

3. Can an altitude be a median?
Definition: An altitude of a triangle is a line segment drawn from any vertex of the triangle to the opposite side, extended if necessary, and perpendicular to that side. (An altitude of a triangle forms right angles with one of the sides.)
Can an altitude be a median?

4. Postulate: Two points determine a line
Auxiliary Lines are additional lines that do not appear in the original diagram. A D B C
If we draw in a line segment from A to D we can prove the triangles congruent by SSS
Given:
Prove:
Postulate: Two points determine a line

5. Given: Prove: Statement Reason C A D B 1. 2. 3. 4. 5. 6. 1. 2. 3. 4.

6. Given: Prove: Reason Statement A D E B C 1. 2. 3. 4. 5. 6. 7. 8. 9. 1.

7. Given: Prove: Reason Statement E H F G 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

8. Given: Prove: Reason Statement S V X T Y Z 1. 2. 3. 4. 5. 6. 7. 8. 9.

9. Summary:
Is CPCTC always the last step? What is the difference between median and an altitude?
Homework: worksheet