1-3: Measuring Segments

Today’s Objectives

Use The Ruler Postulate to calculate lengths of segments

Identify the midpoint of a segment, and apply its properties to solve the length of a segment

Differentiate between congruent segments and equal distances

Ruler Postulate

Postulate 1-5

Every point on a line can be paired with a real number

One-to-one correspondence

A B

Example

Find the distance between the following points.

A and B

B and C

A and D

-8 -6 -4 -2 0 2 4 6 8

A B C DAB = 6

BC = 4

AD = 14

Segment Addition Postulate

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

AB + BC = AC

Example

If EG = 59, what are EF and FG?

E GF

8x-14 4x+1

Set Up an Equation

EF + FG = EG

(8x-14) + (4x+1) = 59 8x-14 + 4x+1 = 59

12x -13 = 59

12x = 72

x = 6

8(6) – 14 4(6)+1

48 – 14 24 +1

EF = 34 EG = 25

Congruent Segments

Congruent Segments – two segments with the same length

Congruent is not the same as equal!

A

B

D

C

Example

What segments are congruent?

-8 -6 -4 -2 0 2 4 6 8

A B C D

𝐴𝐵≌𝐶𝐷 𝐴𝐶≌𝐵𝐷 Congruent SegmentsEqual Distances

Midpoint

Midpoint – the point that divides the segment into two congruent segments

A M B

Congruent Segments

Equal Distances

Midpoint Example

𝑅𝑎𝑦 �⃗�𝐵𝒃𝒊𝒔𝒆𝒄𝒕𝒔 𝑠𝑒𝑔𝑚𝑒𝑛𝑡𝑅𝑃 at point C .What is RP?R

P

C

A

B6 𝑥−7

5 𝑥+1

6 𝑥−7=5𝑥+1

6 𝑥=5 𝑥+8𝑥=8

𝑅𝐶=6 (8 )−7

𝑅𝐶=48−7=41

𝑅𝑃=82

Cut in half