1.2 Use Segments and 1.2 Use Segments and CongruenceCongruence

The Ruler PostulateThe Ruler Postulate

The distance between two points on The distance between two points on a line is the absolute value of the a line is the absolute value of the difference of the coordinates of the difference of the coordinates of the two points.two points.

AB = |AB = |xx22 – – xx11||

x2

BA

x1

Segment Addition PostulateSegment Addition Postulate

If B is between A and C thenIf B is between A and C then

A B C

AB

BC

AC

AAB B

+ BC= AC

Congruent SegmentsCongruent Segments

Two segments are congruent if they Two segments are congruent if they have the same length.have the same length.

A B

C D

12

12

AB is congruent to CD

AB = CD

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Explain what MN means and what MN Explain what MN means and what MN means.means.

If PQ = 4 and QN = 5, what is PN?If PQ = 4 and QN = 5, what is PN?

If MP = 3 and MN = 14, what is PN?If MP = 3 and MN = 14, what is PN?

MN is the line segment MN is the line segment itselfitself

Q NM P

MN means the length of the line MN means the length of the line segmentsegmentPN = PQ + QN = 4 + 5 = 9PN = PQ + QN = 4 + 5 = 9

PN = MN – MP = 14 – 3 = 11PN = MN – MP = 14 – 3 = 11

LM = -6 – (-2)= -6 + 2 = LM = -6 – (-2)= -6 + 2 = ||-4-4| | = 4= 4

JK ≠ LMJK ≠ LM

Plot the points then tell whether the line Plot the points then tell whether the line segments are congruent.segments are congruent.

1. A(0, 1), B(4,1), C(1,2), D(1,6) AB & CD?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?2. J(-6,-8), K(-6,-2), L(-2,-4), M(-6,-4) JK & LM?AB = CDAB = CD

CD = 6 - 2 = CD = 6 - 2 = 44

AB = 4 – 0 = 4AB = 4 – 0 = 4

JK = -2 – (-8) = -2 + 8 = 6JK = -2 – (-8) = -2 + 8 = 6

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