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Measuring Segments

Segments are one of the basics in geometry. You can use algebra to help measure distances between points (coordinates*) on a segment, measure a segment to determine the distance between points, and more! It's really quite simple.

*a coordinate is a point that corresponds to a unique number; think of the Cartesian plane or coordinate plane

Remember learning about absolute value? Well, here's where you will be using it again. The distance between any two points on a segment is the absolute value of the difference of the coordinates. Let's see what this looks like.

Here's a segment, MN, and we want to find the distance between the two points. The coordinates are 3 and 9 so let's use our knowledge of absolute value.

MN = |MN| = |NM| or

MN = |39| = |93| = 6

So, the length or distance between M and N is 6. Easy-peasy, lemon-squeasy!

segmentmeasuring

The Segment Addition Postulate

If B is between A and C, then AC = AB + BC

Segment Addition Postulate

Next up is learning to find the distance/length of a segment. You use algebra to do this! (See? There WAS a reason for taking algebra before geometry!)

Here are two common problems. The first one is strictly algebraic.

Problem #1: B is between A and C, AC = 20 and BC = 12.4. Find AB.

Yikes! What to do!

Step 1: Set up your problem.

What information do you know?

You know that AC = 20.

You also know that BC = 12.4.

You also know that AB + BC = AC. So, let's write this as a problem.

AC = AB + BC

Step 2: Substitute numbers for the variables.

Substitute what you know into your problem.

AC = 20
BC = 12.4

AC = AB + BC

20 = AB + 12.4

AC = AB + BC

20 = AB + 12.4

-12.4 -12.4

7.6 = AB

Step 3: Simplify.

Solve the problem.

Voila! Easy-peasy, lemon-squeasy!

The Segment Addition Property states that AC = AB + BC so by substituting the values you do know and then simplifying, you can find the missing value!

Problem #2: N is between M and O. Find MO.

Goodness! How do you do this one? Again, think of what you know from algebra and the Segment Addition Postulate.

segmentaddition

Step 1: Set up your problem.

What information do you know?

You know that MO = MN + NO.

Looking at the graphic in the problem, you can see that MO = 6x.

You also see that MN = 2x + 4.

So, let's write this as a problem.

MO = MN + NO

Step 2: Substitute numbers for the variables.

Substitute what you know into your problem.

MO = 6x
MN = 2x + 4
NO = 28

MO = MN + NO

6x = (2x + 4) + 28

MO = MN + NO

6x = (2x + 4) + 28

-2x -2x

4x = 4 + 28

4x = 32

4 4

x = 8

Step 3: Simplify.

Solve the problem.

Step 5: Go back and substitute.

Now, go back and substitute the value for what the question is asking for.

Yay! Easy-peasy, lemon-squeasy!

MO = 6x

= 6 • 8

= 48

©2016 Sherry Skipper Spurgeon for Geometry Bugs Me

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