Lesson 3 Segment measure and segment bisector

Two segment with the same length are congruent () segments.      AB = CD (in words, the length of AB is equal to the length of CD) AB  CD (in words, segment AB is congruent to segment CD)

AC = AB + BC Segment Addition Theorem Ex. 1 Use the diagram to find the length of AC. AC = AB + BC Segment Addition Theorem AC = 14 + 6 AC = 20 units

Ex. 2 Use the diagram to find ST.

Ex. 3 Using algebra find the value of x using the diagram Ex. 3 Using algebra find the value of x using the diagram. Also find the lengths of AB and CB.

A midpoint of a line segment is a point that divides the segment into two congruent segments. Ex. 1 Point M is the midpoint of AB. Find AM and MB. We say that M is the midpoint of AB. AM  MB AM  MB Definition of Midpoint AM + MB = AB Seg add thrm x + x = 24cm 2x =24 x = 12cm

Ex. 2 Point P is the midpoint of RS. Find PS and RS. RP PS = 7 cm def of midpoint RS = RP + PS seg add thrm RS = 7cm + 7cm RS= 14 cm

A segment bisector is line segment, ray, line or plane that intersects (crosses) a line segment at its midpoint. To bisect a line segment means to divide the segment into two congruent segments. CD is the bisector of AB. AM  MB

AM MB def of midpoint or def of 5x = 35 x = 35 5 Ex. 3 Line l is a segment bisector of AB. Find the value of x. AM MB def of midpoint or def of seg bisector 5x = 35 x = 35 5 x = 7cm

Ex. 4 Find the coordinates of the midpoint GH. a) G(4, 0), H(-3, -1) = Ex. 4 Find the coordinates of the midpoint GH. a) G(4, 0), H(-3, -1) M = = =

A(5, -4) and B (7, -6) (12/2, -10/2) = (6, -5)

Class work Page 31#1– 6, 13-16 Page 32 #22-28 Omit #26 Pg. 56 – 57 # 2 – 7, 16 – 29 Pg 56 #11-14 Pg 57 # 30, 32, 34 Pg 59 #42, 44