Triangle Inequality Theorem
Triangle Inequality Theorem is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 12: Constructions and Scale Drawings, where students learn and apply the rule that the sum of any two side lengths of a triangle must be greater than the third side, using this theorem to determine whether three given lengths can form a valid triangle. This foundational theorem appears across geometry and is tested in standardized assessments.
Key Concepts
For any triangle with side lengths $a$, $b$, and $c$, the sum of any two sides must be greater than the third side: $$a + b c$$ $$a + c b$$ $$b + c a$$.
Common Questions
What does the Triangle Inequality Theorem state?
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This must hold for all three pairs of sides.
How do you check if three lengths can form a triangle?
Add each pair of two lengths and check that the sum is greater than the remaining length. If all three checks pass, the lengths can form a triangle. If any check fails, they cannot.
Can you check just one pair of sides to test the triangle inequality?
You only need to check whether the sum of the two shorter sides is greater than the longest side. If that holds, the other two inequalities will automatically be satisfied.
What is Big Ideas Math Advanced 2 Chapter 12 about?
Chapter 12 covers Constructions and Scale Drawings, including geometric constructions, properties of special quadrilaterals, angle relationships, and the Triangle Inequality Theorem.