2. Midpoints and Bisectors Vocabulary found in Chapter 1 Section 5 Midpoint, Perpendicular lines, Segment Bisector, Perpendicular Bisector, Angle Bisector. AMB - If AM = MB, then M is the midpoint of AB. - If M is the midpoint of AB, then AM = MB. ~ ~ ~ C 1. If M is the midpoint of AB and B is the midpoint of MC, write an argument of why AM = BC. Include your reasoning. C B DA AB CD (read: AB is perpendicular to CD) If, then all of the angles formed at the point of intersection are right angles. 2. What could you conclude if you were told that two lines intersected to form 90° angles? 60° and 120° angles?

3. - It does not mean that JZ = ZK ~ An angle bisector is a line, segment or ray that divides an angle into two congruent angles. M H T A 1 2 YX K J Z - If JK is a perpendicular bisector of XY, then the angles all measure 90, and Z is the Mid. Pt. of XY. Furthermore XZ = ZY. o ~ A segment bisector is a line, segment or ray that intersects a segment at its midpoint. V SE T O Finish these Statements: E is the Mid. Pt. of SO. SE = EO ~ If E is the Mid. Pt. of SO, then ____________ If TV bisects SO, then ___________________ - If AT is an angle bisector of MAH, then 1 = 2. ~

4. 1.If M is the midpoint of AB, then AM = MB. (By Def. of a Midpoint) If B is the midpoint of MC, then MB = BC. (By Def. of a Midpoint) If AM = MB and MB = BC, then AM = BC by the Transitive Property ~ ~ ~~~ 2.If two lines intersected to form 90° angles, then they are Perpendicular. If two lines intersected to form 60° or 120° angles, then they are not Perpendicular