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Example: Adding and Subtracting lengths $\\$

We are familiar with addition and subtraction of numbers. What is different about adding and subtracting lengths?

The unit!

Lengths are measurements. For example, read the text conversation below:

Remember to take the unit into consideration when subtracting and adding lengths.

For example, 5 miles plus 5 kilometers is not 10 miles, neither is it 10 kilometers. You want to convert one to the other and add. The same goes with subtraction.

Adding and subtracting lengths of collinear segments is a lot like doing addition and subtraction on a number line: a segment of length 9 plus a segment of length 4 yields a segment of length 13, a segment of length 10 minus a segment of length 3 yields a segment of length 7, etc.

Adding and Subtracting Lengths in 2D

Consider the above triangle. AB has length 3, and BC has length 4. What about AC? Here, there are two lengths to consider. The first type of length is easy to calculate: we can get to AC using the two lengths AB + BC, so we find the length of AC to be 3 + 4 = 7.

Do not confuse length with distance: the two lose their synonymy as soon as another segment is introduced. The distance from point A to point C here is 5 (we can use several methods to arrive here: none of which have been developed at this point in the geometry map). Think of distance to be the shortest length between two points.