#### Lesson 4 Measuring Segments

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Lesson 4 Measuring Segments

Ruler Postulate
1-5: The points of a line can be put into a one-to-one
correspondence with the real numbers so that the
distance between any two points is the absolute
value of the difference of the corresponding
numbers.
Practice
Find QS (“the length of segment QS”) if the coordinate
(“location”) of Q is –3 and the coordinate of S is 21.
3 21
24
24
Definition
Congruent: Two segments with the same
length. ()
http://hotmath.com/hotmath_help/topics/congruent-segments/congruent-segments.gif
Practice
Find which two of the segments XY, ZY, and ZW
are congruent.
XY = | –5 – (–1)| = | –4| = 4
ZY = | 2 – (–1)| = |3| = 3
ZW = | 2 – 6| = |–4| = 4
Because XY = ZW, XY
ZW.
Segment Addition Postulate
1-6: If three points A, B, and C are collinear and B is
between A and C, then
AB + BC = AC.
C
B
A
Practice
If AB = 25, find the value of x. Then find AN and NB.
AN + NB = AB
(2x – 6) + (x + 7) = 25
3x + 1 = 25
3x = 24
x=8
AN = 2x – 6 = 2(8) – 6 = 10
NB = x + 7 = (8) + 7 = 15
Practice
If DT = 60, find the value of x. Then find DS and ST.
2x - 8
D
3x - 12
S
T
Definition
Midpoint: a point that divides the segment into
two congruent segments
Segment Bisector: a line, segment, ray, or
plane that intersects a segment at its
midpoint
Practice
M is the midpoint of RT. Find RM, MT, and RT.
RM = MT
5x + 9 = 8x – 36
+36
+36
5x + 45 = 8x
-5x
-5x
45 = 3x
15 = x
RM = 5x + 9 = 5(15) + 9 = 84
MT = 8x – 36 = 8(15) – 36 = 84
RT = RM + MT = 168
Homework
Measuring Segments in
Student Practice Packet
(Page 5, #1-12)