1. 1.2 Linear Measure and Precision

2. 1.2 Linear Measure and Precision
Objectives:
Measure segments and determine accuracy of measurement

3. 1.2 Linear Measure and Precision
Objectives:
Measure segments and determine accuracy of measurement
Compute with measures

4. 1.2 Linear Measure and Precision
A line segment CAN be measured (unlike a line or ray) because it has 2 endpoints

5. 1.2 Linear Measure and Precision
A line segment CAN be measured (unlike a line or ray) because it has 2 endpoints F G m

6. 1.2 Linear Measure and Precision
Precision: Depends on the SMALLEST unit available on the measuring tool.
Measurement should be precise to within 0.5 unit of measure

7. 1.2 Linear Measure and Precision
Precision: Depends on the SMALLEST unit available on the measuring tool.
Measurement should be precise to within 0.5 unit of measure
7 cm means that the ruler was divided into 1 cm – it could be 6.5 cm to 7.5 cm in actual length

8. 1.2 Linear Measure and Precision
Precision: Depends on the SMALLEST unit available on the measuring tool.
Measurement should be precise to within 0.5 unit of measure
8.5 cm means that the ruler was divided into ½ cm – it could be 8.25 cm to 8.75 cm in actual length

9. 1.2 Linear Measure and Precision
Estimate the length of this rectangle.
about 4.5 cm
Smallest unit is 1mm
So precision is ± ½ mm
45 mm ± .5 mm  to 45.5 mm

10. 1.2 Linear Measure and Precision
What does the measurement “5 inches” mean?
1 inch increments
½ of 1 = ½
Range: 5 – ½ = 4.5 in.
5 + ½ = 5.5 in.
8 ½ inches?
½ inch increments, therefore
(½ ) of (½ ) = ¼ in.
Precise to ¼ inch  add ¼ and subtract ¼
Between 8 ¼ to 8 ¾ inches

11. 1.2 Linear Measure and Precision
Measures are real numbers so all operations can be used on them.
Use 2 endpoint letters to show measure of a segment.
AB is a measure – a length
AB = 5 in. DB = 34 in.
AB + DB = = 39 in. CD
Is not a measurement (note bar) A B C D

12. 1.2 Linear Measure and Precision
We know that part + part = whole
This is true for line segments in Geometry –
Called “Segment Addition Postulate” A B
10 cm
4 cm C
part part
= the whole
14 cm

13. 1.2 Linear Measure and Precision
Betweenness of points: for any two real numbers a and b, there is a real number n between a and b such that a < n < b
AB + BC = AC
A, B, C must be collinear and B must be between A and C A B C a n b

14. 1.2 Linear Measure and Precision
Find y and PQ if P is between Q and R; PQ = 2y, QR = 3y + 1, and PR = 21.
P, Q and R are collinear
Draw a figure to represent this information and solve. 21 2y Q P R
Show examples from Interactive 4 a-c
3y + 1
2y + 21 = 3y + 1
20 = y
PQ = 2●20 = 40

15. 1.2 Linear Measure and Precision
Congruent segments: Two segments having the same measure.
If AB = CD, then AB  CD
If AB  CD, then AB = CD B
5 cm D
5 cm A C

16. 1.2 Linear Measure and Precision

17. Homework:
1.2 page multiples of 3,
46-49, 56, 57