1 1-5 Measuring Segments Find the distance between two points using the Ruler Postulate Determine the length of a segment using the Segment Addition Postulate

2 p. 31 TxtBk: Finding Segment Lengths Simulation for measuring segments or hands-on measuring activity with “broken” ruler Ruler Postulate: Given two points, the two points can be paired one to one with two real numbers. The real numbers are called the coordinates of the points To find the distance between the two points, subtract the coordinates; then take the absolute value (to ensure a positive distance)

3 P. 32 TxtBk Ex. 1 Find DE (distance between D and E) Find AB (distance between A and B) DEBAC AB = | -8 – (-5) | = | -3 | = 3 Find BC BC = | -5 – (-2) | = | -3 | = 3 So AB = BC and AB ≅ BC (Congruence of segments)

4 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

5 Example: Segment Addition Postulate PQST Find ST. QS + ST = QT ST = QT – QS ST = 12 – 8 = 4 QT = 12 QS = 8

6 p. 32 TxtBk Ex. 2 DS + ST = DT 2x – 8 + 3x – 12 = 60 5x – 20 = 60 5x = 80 x = 16 DS = 2x – 8 = 2(16) – 8 = 24 ST = 3x – 12 = 3(16) – 12 = 36 DST ST = 3x – 12 DT = 60. Find x, DS, and ST DS = 2x – 8

7 Midpoint of a Segment A midpoint of a segment divides the segment into two congruent segments. The two marks indicate that the two segments are congruent. AB ≅ BC C A B

8 Using the Midpoint AC = CB 2x + 1 = 3x – 4 1 = x – 4 5 = x AC = 2x + 1 = 2(5) + 1 = 11 CB = AC = 11 AB = AC + CB = = 22 AC B 2x + 13x – 4 Given: C is the midpoint of AB. Find AC, CB, and AB.

9 Learning Check and Summary Suppose X, Y, and Z are collinear. If XY = 10 and XZ = 6 and YZ = 4, which point lies between the other two points? The midpoint of a segments splits the segment into two ___?___ segments