1-2 Measuring and Constructing Segments

1-2 Measuring and Constructing Segments

Coordinate—A number used to identify the location of a point. On a number line, only one coordinate is used. On the coordinate plane, two coordinates are used, the x-coordinate and the y-coordinate. In space, three coordinates are used, the x-coordinate, y-coordinate and z-coordinate.

Ruler Postulate—The points on a line can be put into a one-to-one correspondence with real numbers.

Distance-between two points is the absolute value of the difference of the coordinates of the points. Distance will always be positive in this class. If the coordinates are A and B, with the value being a and b, then the distance is

. Since it is absolute value, the answer would be the same.

This is also called the length of or AB

Ex A is at 9, B is at 5, so the distance would be

Congruent segments-segments which have the same length.

are congruent line segments

We use tick marks to show congruence.

represent geometric figures. CD and PN are distance or lengths.

When we do this, it means that the length of CD is the same as the length of PN

Now let CD = 5. Notice I did not put the line above the CD. This is because I am now dealing with distance. Distance is a number, the actual size of the segment. So I use the equal sign.

Now if CD = 5. What does PN = ?

Therefore CD = PN (again dealing with distance)

When we do not know the distance (length) or measurement,

we use the congruent mark.

Think of it as:

“pictures are

“numbers are =”

Again, EF names a segment whose endpoints are E and F.

When there is no line above the points, EF refers to the length of the segment.

Construction—a way of creating a figure that is more precise. We will use a compass and a straightedge. On the computer, we will use a Geogebra.

Between—Given three points, A, B, and C, B is between A and C if and only if all three points lie on the same line and AB + BC = AC. B does not have to be in the middle of the line segment.

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

Bisect—To divide into two congruent parts

Midpoint—the point that divides the segment into two congruent segments. If M is the midpoint of , then AM = BM

Segment bisector-a ray, segment, or line that intersects a segment at its midpoint. It divides the segment into two equal parts at its midpoint.

Notice that in the last example, the segments bisect each other. Do not assume anything. Look for the tick marks, or if the lengths are given may you assume they are congruent!!!!!