Section 1-4: Measuring Segments SPI 12A: Use absolute value to express distance between two points SPI 21B: Solve multi-step.

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Section 1-4: Measuring Segments SPI 12A: Use absolute value to express distance between two points SPI 21B: Solve multi-step linear equations to find length, width, perimeter and area of geometric figures SPI 32A: Identify properties of plane figures from information in a diagram Objectives: Find the lengths of segments by using: 1. Ruler Postulate 2. Segment Addition Postulate 3. Midpoint

Absolute Value and the Ruler Postulate The points of a line can be put into one to one correspondence with real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers. Postulate 1-5 You can use the Ruler Postulate to find the distanced between points on the number line. The distance between A and B is 4 (absolute value) A B The length of AB AB = |4 - 8| = 4 Note: The length of a segment is indicated by the endpoints of the segment without the bar over it… AB indicates segment AB AB means to find the length of AB (number)

Using the Ruler Postulate A B C D E 1) Find AC AC = |-6 - 0| = 6 2) Find BE BE = |-3 - 4| = 7 3) Find DB DB = |1 – (-3)| = 4 4) Find AD AD = |-6 - 1| = 7 Which of the above examples have the same length? AD and BE have the same length, so they are congruent Congruent Segments two segments that have the same length Symbol for congruence: 

Segment Addition Postulate If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC. Postulate 1-6 A B C Postulate: If C is between A and B, then AC + CB = AB. Example: If AC = x , CB = 2x and AB = 12, then Find x, AC and CB. 2x x 12 AC + CB = AB x + 2x = 12 3x = 12 x = 4 x = 4 AC = 4 CB = 8

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

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

Processing Midpoint Pairs Exercise 8.5 8 10 10 25 13