# Geometry Section 1.3 Measuring Lengths

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Geometry Section 1.3 Measuring Lengths

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

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

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

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

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

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.

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

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

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.

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

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

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