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SOME THEOREMS AND POSTULATES Fernando Rodriguez Buena Park HS [email protected] Presented at CMC South Palm Springs, CA Nov. 4, 2005 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. | A | | AC B AB | C BC | A segment bisector is a segment, ray, line, or plane that intersects a segment at its midpoint. A M B M is the midpoint of AB if M is on AB and AM = MB. C M A B D CD is a bisector of AB. Bisecting An Angle An angle bisector is a ray that divides an angle into two adjacent angles that are congruent. In the diagram ray CD bisects ABC because it divides the angle into two congruent angles, _____ and _____. A D C B mACD mBCD To write “ AB is Parallel to CD “ A C you write AB || CD B D 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 . 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 . Given that m1 32, find each measure. Tell which postulate or theorem you use. a. m2 b. m3 c. m4 d. m5 m2 32 Corresponding Angle Postulate m3 32 Alternate Exterior Angle Postulate m4 1803 148 Linear Pair Postulate m5 32 Vertical Angle Theorem 1 5 4 3 2 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 C H I B A HI AB 1 HI AB 2