Chapter 1 Basics of Geometry

Section 5 Segments and Their Measures

The points on a line can be matched one to one with the real numbers 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 points. In the diagram, x1 and x2 are coordinates. The small numbers are subscripts. The coordinates are read as “x sub 1” and “x sub 2”. The distance between points A and B is written as AB. It is the absolute value of the difference of the coordinates of A and B. AB is also called the length of AB.

Example 1: Find the Distance Between Two Points Measure the total length of the shark’s tooth to the nearest 1/8 inch. Then measure the length of the exposed part.

Checkpoint: Find the Distance Between Two Points Measure the length of the segment to the nearest 1/8 inch.

When three points lie on a line, one of them is between the other two When three points lie on a line, one of them is between the other two. In the diagram of Postulate 5 below, B is between A and C.

Example 2: Find a Distance by Adding Use the map to find the distance from Athens to Albany.

Example 3: Find a Distance by Subtracting Use the diagram to find EF.

Checkpoint: Use the Segment Addition Postulate Find the length.

Congruence In geometry, segments that have the same length are called ______________________________.

Example 4: Decide Whether Segments are Congruent Are the segments shown in the coordinate plane congruent?

Checkpoint: Decide Whether Segments are Congruent Plot the points in a coordinate plane. Then decide whether AB and CD are congruent. 1. A (-2, 3), B(3, 3), C(-3, 4), D(-3, -1) 2. A(0, 5), B(0, -1), C(5, 0), D(-1, 0)