1.2 Use Segments and Congruence

The Ruler Postulate The distance between two points on a line is the absolute value of the difference of the coordinates of the two points. AB = |x2 – x1| A B x1 x2

Segment Addition Postulate If B is between A and C then AB + BC = AC AC AB BC A B C

Congruent Segments Two segments are congruent if they have the same length. A 12 B C D 12 AB is congruent to CD AB = CD ~

If PQ = 4 and QN = 5, what is PN? If MP = 3 and MN = 14, what is PN? Explain what MN means and what MN means. If PQ = 4 and QN = 5, what is PN? If MP = 3 and MN = 14, what is PN? M P Q N MN is the line segment itself MN means the length of the line segment PN = PQ + QN = 4 + 5 = 9 PN = MN – MP = 14 – 3 = 11

Plot the points then tell whether the line segments are congruent. 1. A(0, 1), B(4,1), C(1,2), D(1,6) AB & CD? 2. J(-6,-8), K(-6,-2), L(-2,-4), M(-6,-4) JK & LM? AB = 4 – 0 = 4 CD = 6 - 2 = 4 AB = CD ~ JK = -2 – (-8) = -2 + 8 = 6 LM = -6 – (-2)= -6 + 2 = |-4| = 4 ~ JK ≠ LM