Inequality theorem (l4)
Transcript of Inequality theorem (l4)
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INEQUALITY THEOREM
Module 6 Lesson 4
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What is the triangle inequality theorem? ◦ According the regentsprep.org, “The sum of the lengths of any two sides of a
triangle must be greater than the third side.”
◦What does that mean? Add any 2 lengths of a triangle together and it will be greater than the 3rd side.
◦ http://www.regentsprep.org/regents/math/geometry/GP7/LTriIneq.htm
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So what does that mean?◦ If you are given two sides of a triangle, you can find the range of the 3rd side.
◦ If you have three numbers, you can determine if it would make a triangle or not.
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Try these…◦ Two sides of a triangle are 10 and 13. Find the range of possible measures of the 3rd
side.
◦Given the sides: 1, 2 and 3, does it form a triangle?
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Answers….◦ 3<x<23…subtract the sides to get 3. The 3rd side has to be greater than that. Add
the sides and the 3rd side must be less than that.
◦No, 1+2=3. The 2 sides added together must be greater than the 3rd. 3+2>1 and 3+1>2 but 1+2 isn’t greater than 3.
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Bonus question◦ This one is a most missed questions on the mastery assignment. Try it and check
your answer.
◦Write an inequality, describing x.
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Answer◦ Since the angle 86 is less than the right angle, the side across from 86 (3x+7) is
less than the side across from the right angle(5x+9).