1.3 Segments and Their Measures

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Presentation transcript:

1.3 Segments and Their Measures Geometry Mrs. Spitz Spring 2005

Objectives/Assignment Use segment postulates. Use the Distance Formula to measure distances as applied. Assignment: pp. 21-23 #1-51 all

Using Segment Postulates In geometry, rules that are accepted without proof are called postulates, or axioms. Rules that are proved are called theorems. In this lesson, you will study two postulates about the lengths of segments.

Example what your note page should look like now Name____________________________ Date___________________Period_____ Class_____________________________ 1.3 Segments & Their Measures Objectives: Assignment: Using Segment Postulates Use segment postulates. Use the Distance Formula to measure distances as applied. pp. 21-23 #1-51 all In geometry, rules that are accepted without proof are called postulates, or axioms. Rules that are proved are called theorems.

Postulate 1: Ruler Postulate B x1 x2 Names of points Coordinates of points The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. The distance between points A and B written as AB, is the absolute value of the difference between the coordinates of A and B. AB is also called the length of AB. A AB B x1 x2 AB = |x2 – x1|

Ex. 1: Finding the Distance Between Two Points Measure the length of the segment to the nearest millimeter. Solution: Use a metric ruler. Align one mark of the ruler with A. Then estimate the coordinate of B. For example if you align A with 3, B appears to align with 5.5. The distance between A and B is about 2.5 cm. AB = |5.5 – 3| = |2.5| = 2.5

Note: It doesn’t matter how you place the ruler. For example, if the ruler in Example 1 is placed so that A is aligned with 4, then B align 6.5. The difference in the coordinates is the same.

Note: A Point B is between points A and C. When three points lie on a line, you can say that one of them is between the other two. This concept applies to collinear points only. For instance, in the figures on the next slide, point B is between points A and C, but point E is not between points D and F. B C D E Point E is NOT between points D and F. F

Postulate 2: Segment Addition Postulate If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C. AC A B C AB BC

Ex. 2: Finding Distances on a Map Map Reading. Use the map to find the distances between the three cities that lie on a line.