1. SOME THEOREMS AND POSTULATES Fernando Rodriguez Buena Park HS frodriguez@fjuhsd.k12.ca.us Presented at CMC South Palm Springs, CA Nov. 4, 2005

2. Postulate 2 Segment Addition Postulate If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C. ACB | | AC | | | AB BC

3. A segment bisector is a segment, ray, line, or plane that intersects a segment at its midpoint. M is the midpoint of if M is on and AM = MB. is a bisector of.

4. Bisecting An Angle An angle bisector is a ray that divides an angle into two adjacent angles that are congruent. In the diagram ray bisects because it divides the angle into two congruent angles, _____ and _____.

5. To write “ AB is Parallel to CD “ you write AB || CD A D C B

6. Parallel and Perpendicular Postulates POSTULATE 13 Parallel Postulate If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. P There is exactly one line through P parallel to.

7. Parallel and Perpendicular Postulates POSTULATE 14 Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. P There is exactly one line through P perpendicular to.

8. Given that, find each measure. Tell which postulate or theorem you use. a. b. c. d. 2 1 4 5 3 Corresponding Angle Postulate Alternate Exterior Angle Postulate Linear Pair Postulate Vertical Angle Theorem

9. Theorem 5.9 Midsegment theorem The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long