Triangle inequality theorem

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