1.2 Linear Measure and Precision

Objectives: Measure segments and determine accuracy of measurement. Measure segments and determine accuracy of measurement. Compute with measures. Compute with measures.

Segments A line segment or segment AB (or BA) consists of the endpoints A and B, and all points on AB that are between A and B. Line segments have exact measures but can only be as precise as the smallest unit of the measuring device. A line segment or segment AB (or BA) consists of the endpoints A and B, and all points on AB that are between A and B. Line segments have exact measures but can only be as precise as the smallest unit of the measuring device. l Line l or AB A C B D Segment CD

Precision The precision of any measurement depends on the measuring tool. The measurement should be within 0.5 unit of the measure. Thus, if AB is measured in inches and is 2” long, its precision is 1.5” to 2.5”. The precision of any measurement depends on the measuring tool. The measurement should be within 0.5 unit of the measure. Thus, if AB is measured in inches and is 2” long, its precision is 1.5” to 2.5”. l Line l or AB A B

Measures Measures are real numbers, thus all arithmetic properties can be applied. Measures are real numbers, thus all arithmetic properties can be applied. If we have a line segment divided into parts, then by applying a relationship called betweenness of points we know the measure of each segment added together equals the measurement of the entire segment. If we have a line segment divided into parts, then by applying a relationship called betweenness of points we know the measure of each segment added together equals the measurement of the entire segment. AB + BC = AC AB + BC = AC ABC

Congruent Segments When segments have the same measure, they are said to be congruent (  ). When segments have the same measure, they are said to be congruent (  ).  is read “is congruent to.” Slashes on the line segments also indicate the segments are congruent.  is read “is congruent to.” Slashes on the line segments also indicate the segments are congruent. AB  CD AB  CD AB C D

More About Congruency Note, when we are discussing segments we draw a line over the endpoints, AB, but when we are discussing the measure of segments we simply write the letters. Likewise, we must also be sure that when we are comparing segments we use the congruent sign, but when we are comparing their measures we use an equal sign. Note, when we are discussing segments we draw a line over the endpoints, AB, but when we are discussing the measure of segments we simply write the letters. Likewise, we must also be sure that when we are comparing segments we use the congruent sign, but when we are comparing their measures we use an equal sign. Never intermix the two symbols. Never intermix the two symbols. AB  CDsegments AB = CD measures

Assignment: Geometry Geometry Pg. 17, #12 – 18, 22 – 39 Pre-AP Geometry Pre-AP Geometry Pg. 17 – 19, #12 – 39 & 50