1 / 7

Section 1-3: Measuring Segments

Section 1-3: Measuring Segments. Objectives: Find the lengths of segments by using: 1. Ruler Postulate 2. Segment Addition Postulate 3. Midpoint. AB indicates segment AB. AB means to find the length of AB (number). Absolute Value and the Ruler Postulate.

helene
Download Presentation

Section 1-3: Measuring Segments

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 1-3: Measuring Segments • Objectives: • Find the lengths of segments by using: • 1. Ruler Postulate • 2. Segment Addition Postulate • 3. Midpoint

  2. AB indicates segment AB AB means to find the length of AB (number) Absolute Value and the Ruler Postulate 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…

  3. A B C D E AD and BE have the same length, so they are congruent Using the Ruler Postulate 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? • Congruent Segments • two segments that have the same length • Symbol for congruence: 

  4. 12 AC + CB = AB x + 2x = 12 3x = 12 x = 4 Segment Addition Postulate 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 x = 4 AC = 4 CB = 8

  5. AN = 2x – 6 = 2(8) – 6 = 10 NB = x + 7 = (8) + 7 = 15 Substitute 8 for x. 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 = ABSegment 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 = 10 and NB = 15, which checks because the sum of the segment lengths equals 25.

  6. RM = MTDefinition of midpoint 5x + 9 = 8x – 36Substitute. 5x + 45 = 8xAdd 36 to each side. 45 = 3xSubtract 5x from each side. 15 = xDivide each side by 3. RM = 5x + 9 = 5(15) + 9 = 84 MT = 8x – 36 = 8(15) – 36 = 84 Substitute 15 for x. 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. RT = RM + MT = 168 RM and MT are each 84, which is half of 168, the length of RT.

  7. Processing Midpoint Pairs Exercise 8.5 8 10 10 25 13

More Related