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Geometry Section 1.3 Measuring Lengths. Consider this number line. On a number line, the real number assigned to a point is called the _________ of the.

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Presentation on theme: "Geometry Section 1.3 Measuring Lengths. Consider this number line. On a number line, the real number assigned to a point is called the _________ of the."— Presentation transcript:

1 Geometry Section 1.3 Measuring 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 larger coordinate minus the smaller coordinate. For the previous problem.

4 The distance between the two points C and H is the same as the length of, which can be written as ____. (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 Two segments are congruent if they have the same length. “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. Postulate 2: 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. BC= 33 1/3 AC= 46 1/3

12 The Distance Formula and Midpoint Formula For any two points AB = the midpoint of AB =

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


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