Range of Possible Lengths for a Third Side
Range of Possible Lengths for a Third Side is a Grade 7 math skill in Reveal Math Accelerated, Unit 11: Angles, where students apply the Triangle Inequality Theorem to determine all valid lengths for an unknown third side when two side lengths are known, expressing the answer as a range (difference < third side < sum). This skill is essential for understanding when a valid triangle can be formed.
Key Concepts
Given two side lengths of a triangle, $a$ and $b$, the length of the third side, $c$, must be strictly greater than their positive difference and strictly less than their sum: $$|a b| < c < a + b$$.
Common Questions
How do you find the range of possible lengths for a third side?
If the two known sides are a and b, the third side c must satisfy: |a - b| < c < a + b. The third side must be longer than the difference of the other two sides and shorter than their sum.
What is the Triangle Inequality Theorem?
The Triangle Inequality Theorem states that the sum of any two side lengths of a triangle must be greater than the third side length. This ensures that the three sides can actually form a closed triangle.
What happens if the third side equals the sum of the other two?
If c = a + b exactly, the triangle degenerates into a straight line (three collinear points), which is not a valid triangle. The inequality is strict: c must be strictly less than a + b.
What is Reveal Math Accelerated Unit 11 about?
Unit 11 covers Angles, including angle relationships with parallel lines and transversals, triangle angle-sum and exterior angle theorems, and the Triangle Inequality Theorem.