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- 1. INEQUALITY THEOREM Module 6 Lesson 4
- 2. 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
- 3. 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.
- 4. 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?
- 5. 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.
- 6. Bonus question ◦ This one is a most missed questions on the mastery assignment. Try it and check your answer. ◦ Write an inequality, describing x.
- 7. 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). ◦ 3𝑥 + 7 < 5𝑥 + 9 ◦ −5𝑥 − 5𝑥 ◦ −2𝑥 + 7 < 9 ◦ −7 − 7 ◦ −2𝑥 < 2 ◦ ÷ −2 ÷ −2 ◦ 𝑥 ≻ −1

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