Measuring Segments

GeometryMrs. King

Unit 1, Lesson 4

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.

213

24

24

Definition

Congruent: Two segments with the same length. ()

http://hotmath.com/hotmath_help/topics/congruent-segments/congruent-segments.gif

XY = | –5 – (–1)| = | –4| = 4

ZY = | 2 – (–1)| = |3| = 3

ZW = | 2 – 6| = |–4| = 4

Find which two of the segments XY, ZY, and ZW

are congruent.

Because XY = ZW, XY ZW.

Practice

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.

A

B

C

AN + NB = AB(2x – 6) + (x + 7) = 25

3x + 1 = 25 3x = 24 x = 8

If AB = 25, find the value of x. Then find AN and NB.

AN = 2x – 6 = 2(8) – 6 = 10 NB = x + 7 = (8) + 7 = 15

Practice

PracticeIf DT = 60, find the value of x. Then find DS and ST.

D S T

2x - 8 3x - 12

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

RM = MT5x + 9 = 8x – 36

+36 +365x + 45 = 8x -5x -5x 45 = 3x 15 = x

M is the midpoint of RT. Find RM, MT, and RT.

RM = 5x + 9 = 5(15) + 9 = 84MT = 8x – 36 = 8(15) – 36 = 84

RT = RM + MT = 168

Practice

Homework

Measuring Segments in Student Practice Packet(Page 5, #1-12)