Linear Measure

Objective: (1)To measure segments and determine accuracy of measurement.

(2) To compute with measures.

Definitions• Line segment: A measureable part of a line that consists of two

points, called endpoints, and all of the points between them.• Precision: The precision of any measurement depends on the

smallest unit available on the measuring tool• Betweeness of points:• Between: For any two points A and B on a line, there is another

point C between A and B if and only if A, B, and C are collinear and AC + CB = AB

• Constructions: A method of creating geometric figures without the benefit of measuring tools. Generally, only a pencil, straightedge, and a compass are used.

• Congruent: Having the same size and same shape.

Line Segments

• Consists of two endpoints

• And all points in between

• Has an infinite number of points.

• Since it is finite, it has a distance.

• Named by the endpoints– AB or BA

•A

•B

Symbols Review

ABAaABHere’s a new one:AB

Line ABA or Point ALine aSegment AB

The Length of Segment AB

Betweeness of Points

• Point M is between points P and Q if and only if P, Q and M are collinear & if:

PM + MQ = PQ• Notice that M is

between but not in the middle! There’s a difference.

PQ• ••

M

Finding the Distance

Find AB if AC = 19cm and BC = 12cmSince we don’t know what AB is, we’ll say, AB = xWe also know:AB+BC=AC … now replacex + 12 = 19 -12 -12x = 7

A

B

C

12cm

19cm

x cm

Another way to find the distance

• Find x if: AB = 5x+7, BC = 3x + 2 and AC = 33mPlug in what you knowAlso AB+BC=AC5x + 7 + 3x + 2 = 338x + 9 = 33 -9 -98x = 24

A

BC

5x + 7

3x + 2

33cm

Continued

8x = 248 8x = 3Now, just in case you’re asked to find AB or BC.Replace the variable with 3

A

BC

5x + 7

3x + 2

33cm

3(3) + 29 + 211

5(3) + 715 + 722