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Lesson 156: Relationship Between Sides of a Triangle
This quick lesson introduces a very easy topic that frequently shows up on math exit exams and standardized exams such as the SAT.
Here
is a typical question: Two sides of a triangle measure 2cm and
5cm. What is a possible measurement of the third side?
Sometimes you'll be given multiple choice, and sometimes you'll have
to represent the possible range of answers. Look at the
diagram at left.
In the upper picture, I've arranged the two sides so that they are separated quite far apart. Notice that the missing side cannot possibly be larger than 7, which is the sum of the two sides. If it was, then it would not be able to connect to the other two sides. It can't be equal to 7 either. If it was, then the two other sides would have to be lying flat along a straight line, and of course we then wouldn't have a triangle. They have to be angled at least slightly. This means that x < 7.
Now let's look at the lower picture. I've arranged the sides so that they are quite close together, forming a small angle. Notice that x must be greater than 3, which is the difference of the two sides. If it was less than 3, it would be too short to connect. If it was exactly 3, then the sides of 2 and 5 would actually be on top of each other, and that wouldn't be a triangle anymore. The sides of 2 and 5 must be angled at least slightly. This means that x > 3.
We can say that 3 < x < 7. This means that x must be between 3 and 7, but not equal to either. Any answer within this range will be correct.
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