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**Geometry Section 1.3 Measuring Lengths**

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**Consider this number line**

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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To find the distance between two points on a number line, take the larger coordinate minus the smaller coordinate. For the previous problem.

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

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**Consider this number line. Examples: Find the distances. AB = _______**

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

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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

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**Two segments are congruent if they have the same length**

Two segments are congruent if they have the same length. “Tick” marks are used to indicate congruent segments in a figure.

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

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

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**On the number line at the top of the page, we determined that**

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.

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

Example: B is between A and C, AB = 13, BC = 5x and AC = 8x – 7. Determine x, BC and AC. 5𝑥+13=8𝑥−7 BC= 33 1/3 AC= 46 1/3 20=3𝑥 𝑥=20/3

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

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

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4.1 Apply the Distance and Midpoint Formulas The Distance Formula: d = Find the distance between the points: (4, -1), (-1, 6)

4.1 Apply the Distance and Midpoint Formulas The Distance Formula: d = Find the distance between the points: (4, -1), (-1, 6)

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