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 AB A a Here’s a new one: Line AB A or Point A Line a Segment 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. P • • Q • M

Finding the Distance Find AB if AC = 19cm and BC = 12cm  x cm Find AB if AC = 19cm and BC = 12cm Since we don’t know what AB is, we’ll say, AB = x We also know: AB+BC=AC … now replace x + 12 = 19 -12 -12 x = 7 B  12cm 19cm C

Another way to find the distance Find x if: AB = 5x+7, BC = 3x + 2 and AC = 33m Plug in what you know Also AB+BC=AC 5x + 7 + 3x + 2 = 33 8x + 9 = 33 -9 -9 8x = 24 3x + 2 B  33cm 5x + 7 A

Continued C 8x = 24 8 x = 3 Now, just in case you’re asked to find AB or BC. Replace the variable with 3 3x + 2 3(3) + 2 9 + 2 11 B  33cm 5(3) + 7 22 5x + 7 15 + 7 A