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Honors Geometry Section 1.2 Measuring Lengths

Honors Geometry Section 1.2 Measuring Lengths. Consider this number line . On a number line, the real number assigned to a point is called the _________ of the point. Find the distance between C and H. coordinate.

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Honors Geometry Section 1.2 Measuring Lengths

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  1. Honors Geometry Section 1.2Measuring Lengths

  2. Consider this number line.On a number line, the real number assigned to a point is called the _________ of the point.Find the distance between C and H. coordinate

  3. To find the distance between two points on a number line, take the absolute value of the difference between the coordinates. For the previous problem.

  4. The distance between the two points C and H is the same as the length of , which can be writtenas ____ . (Note: _________________).

  5. Consider this number line.Examples: Find the distances. AB = _______ GH = ________ HI= ________ GI = ________

  6. While we are permitted to say AB = GH, we cannot say because they are not the exact same set of points. Instead we write is congruent to

  7. Postulate 1.2.2: If two segments have equal lengths, then they are congruent.“Tick” marks are used to indicate congruent segments in a figure.

  8. A *midpoint of a segment is the point that divides the segment into two congruent segments.

  9. Example: On the number line at the top of the page, if I is the midpoint of , what is the coordinate of point J?

  10. On the number line at the top of the page, we determined that .This illustrates the next postulate.Postulate1.2.3: Segment Addition Postulate: If R is between P and Q, then ______________Note: In order for one point to be between two other points, the points must be collinear.

  11. Example: B is between A and C, AB= 13, BC = 5x and AC = 8x – 7. Determine x, BC and AC.

  12. The Distance Formula and Midpoint FormulaFor any two pointsAB = the midpoint of AB =

  13. Example: If A(-3, 7) and B(9, -2), find AB and the midpoint of .

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