How to find the lengths of segments. Chapter 1.5GeometryStandard/Goal 2.2

1. Check and discuss assignment from yesterday. 2. Work on Quiz Read, write, and discuss how to find lengths of segments. 4. Work on assignment.

The points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers.

coordinate is its distance and direction from the origin of a number line. Congruent segments is two segments with the same length. Example:

Use the Ruler Postulate to find the length of each segment. XY = | –5 – (–1)| = | –4| = 4 ZY = | 2 – (–1)| = |3| = 3 ZW = | 2 – 6| = |–4| = 4 Find which two of the segments XY, ZY, and ZW are congruent. Because XY = ZW, XY ZW.

If three points A, B, and C are collinear and B is between A and C, Then AB + BC = AC

Use the Segment Addition Postulate to write an equation. AN + NB = AB Segment Addition Postulate (2 x – 6) + ( x + 7) = 25 Substitute. 3 x + 1 = 25Simplify the left side. 3 x = 24Subtract 1 from each side. x = 8Divide each side by 3. AN = 10 and NB = 15, which checks because the sum of the segment lengths equals 25. If AB = 25, find the value of x. Then find AN and NB. AN = 2 x – 6 = 2(8) – 6 = 10 NB = x + 7 = (8) + 7 = 15 Substitute 8 for x.

midpoint of a segment is a point that divides the segment into two congruent segments. ACB

Use the definition of midpoint to write an equation. RM = MT Definition of midpoint 5 x + 9 = 8 x – 36Substitute. 5 x + 45 = 8 x Add 36 to each side. 45 = 3 x Subtract 5 x from each side. 15 = x Divide each side by 3. RM and MT are each 84, which is half of 168, the length of RT. M is the midpoint of RT. Find RM, MT, and RT. RM = 5 x + 9 = 5(15) + 9 = 84 MT = 8 x – 36 = 8(15) – 36 = 84 Substitute 15 for x. RT = RM + MT = 168 Segment Addition Postulate

Kennedy, D., Charles, R., Hall, B., Bass, L., Johnson, A. (2009) Geometry Prentice Hall Mathematics. Power Point made by: Robert Orloski Jerome High School.