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

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.

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 = _______ 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

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.

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. 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.

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

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.