On the previous page, you learned about how the converse of the Triangle Inequality Theorem can help you determine if a set of three length measurements represents a triangle, or not. Imagining a shape consisting of sides of those lengths is actually easier than calculating all three inequalities from the theorem. In the exercise below, see if you can determine whether the dimensions are triangles, based on the information provided.
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Given these measurements: 24 inches, 13 inches, and 5 inches
Can sides or segments with these three lengths form a triangle? |
yes
no
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Remember, no side can be longer than or equal to the other two side lengths added together.
Remember, no side can be longer than or equal to the other two side lengths added together.
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Given: 7.6 cm, 7.6 cm, 7.6 cm.
Can sides of these lengths form a triangle? |
yes
no
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Can you say that EVERY number is less than the sum of the other two numbers? If so, then you have a triangle.
Can you say that EVERY number is less than the sum of the other two numbers? If so, then you have a triangle.
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Given three sides of these lengths: 12 yd, 13 yd, and 28 yd
Can the sides form a triangle? |
yes
no
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If you can find one number that is actually greater than the sum of the other two numbers, then there is no triangle.
If you can find one number that is actually greater than the sum of the other two numbers, then there is no triangle.
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Given: 5 inches, 13 inches, 10 inches
Do you have the measurements needed to form a triangle? |
yes
no
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If EVERY number is smaller than the sum of the other two, then it is a triangle.
If EVERY number is smaller than the sum of the other two, then it is a triangle.
Complete
