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Notes 1.2

Notes 1.2. Measuring and Constructing Segments. Distance. The Distance between any 2 points is the absolute value of the difference of the coordinates. BC = |C – B| = |3 – 1| = 2 AC = |C – A| = |3 - -2| = |3 + 2| = 5. Congruent Segments.

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Notes 1.2

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  1. Notes 1.2 Measuring and Constructing Segments

  2. Distance • The Distance between any 2 points is the absolute value of the difference of the coordinates. • BC = |C – B| = |3 – 1| = 2 • AC = |C – A| = |3 - -2| = |3 + 2| = 5

  3. Congruent Segments • Congruent Segments are segments that have the same sizw and same shape. • Tick Marks are used to show congruence.

  4. SEGMENT ADDITION POSTULATE • If B is between A and C, • • • • A B C then AB + BC = AC.

  5. – 3x – 3x –2 –2 2 2 EXAMPLE # 1 Using the Segment Addition Postulate M is between N and O. Find X. NM + MO = NO 17 + (3x – 5) = 5x + 2 3x + 12 = 5x + 2 12 = 2x + 2 10 = 2x 5 = x

  6. – 3x – 3x 12 = 3x 3 3 EXAMPLE # 2 Using the Segment Addition Postulate E is between D and F. Find DF. DE + EF = DF (3x – 1) + 13 = 6x 3x + 12 = 6x 12 = 3x 4 = x

  7. EXAMPLE # 2 Continued Using the Segment Addition Postulate E is between D and F. Find DF. DF = 6x = 6(4) = 24

  8. Midpoints • The midpointM of AB is the point that bisects, or divides, the segment into two congruent segments. • Example: • If M is the midpoint of AB, then AM = MB. • So if AB = 6, then AM = 3 and MB = 3.

  9. D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. 15 = 3x 3 3 –4x –4x +9 + 9 Example 3: Using Midpoints to Find Lengths E D 4x + 6 7x – 9 F Step 1 Solve for x. ED = DF 4x + 6 = 7x – 9 6 = 3x – 9 x = 5 15 = 3x

  10. D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. Example 3 Continued E D 4x + 6 F 7x – 9 Step 2 Find ED, DF, and EF. ED = 4x + 6 DF = 7x – 9 EF = ED + DF = 4(5) + 6 = 7(5) – 9 = 26 + 26 = 52 = 26 = 26

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