Measuring Segments Skill 03

Objective HSG-GPE.6: Students are responsible for finding and comparing lengths of segments.

Definitions The real number that corresponds to a point is called the coordinate of the point. The distance between two points is the absolute value of the difference of their coordinates. If two segments have the same length, then the segments are congruent.

Definitions The midpoint of a segment is a point that divides the segment into two congruent segments. A point, ray, line, or other segment that intersects a segment at its midpoint is the segment bisector.

Postulate 5 -1.5 1 π The Ruler Postulate Every point on a line can be paired with a real number. This makes a 1-to-1 correspondence between points on a line and the real number line. -1.5 1 π

Postulate 6 A B C The Segment Addition Postulate If three points A, B, and C, are collinear and B is between A and C, then AB + BC = AC. A B C

Example 1; Measuring Segment Lengths a) What is 𝑆𝑇? b) What is 𝑈𝑉? c) What is 𝑆𝑉? -6 -2 2 6 10 14 18 S T U V

Example 2; Segment Addition Postulate If 𝐸𝐺=59, what are 𝐸𝐹 and 𝐹𝐺? 𝟖𝒙−𝟏𝟒 𝟒𝒙+𝟏 E F G

Example 3; Comparing Segment Lenths a) Are 𝐴𝐶 and 𝐵𝐷 congruent? b) Is 𝐴𝐵 congruent to 𝐷𝐸 ? -6 -2 2 6 10 14 18 A B C D E

Example 4; Using the Midpoint 𝑄 is the midpoint of 𝑃𝑅 . What are 𝑃𝑄, 𝑄𝑅, and 𝑃𝑅? 𝟔𝒙−𝟕 𝟓𝒙+𝟏 E F G

#03: Measuring Segments Questions? Summarize Notes Homework Video Quiz