Classify Triangles by Side Lengths (Triangle Inequality Theorem)
Classify Triangles by Side Lengths (Triangle Inequality Theorem) is a Grade 5 math skill from Illustrative Mathematics Chapter 7 (Shapes on the Coordinate Plane) that teaches the Triangle Inequality: the sum of any two sides must be strictly greater than the third side for a triangle to exist. If the two shorter sides together are less than or equal to the longest side, no valid triangle can be formed.
Key Concepts
Property To determine if a triangle is possible at all, check the Side Length Condition (Triangle Inequality): The sum of the lengths of any two sides must be strictly greater than the length of the third side. If the sum of the two shorter sides is less than or equal to the longest side, no triangle is formed.
Examples Side lengths of 2 cm, 3 cm, and 7 cm cannot form a triangle because 2 + 3 < 7. The two shorter sides are not long enough to meet. Given side lengths of 3, 4, and 8, since 3 + 4 is less than or equal to 8, the two shorter sides are not long enough to connect, so no triangle is formed.
Explanation When constructing a triangle, the given measurements act as a set of instructions. If the side lengths are too short to connect, no triangle can be formed. The two smaller sides combined must always be longer than the biggest side, otherwise, they will just collapse flat!
Common Questions
What is the Triangle Inequality Theorem?
The Triangle Inequality states that for a valid triangle, the sum of the lengths of any two sides must be strictly greater than the length of the third side. If the two shorter sides add up to less than or equal to the longest side, no triangle is possible.
How do you check if three side lengths can form a triangle?
Add the two shorter sides and compare to the longest side. If their sum is greater than the longest side, a triangle is possible. If their sum is less than or equal to the longest side, no triangle can be formed.
What chapter covers the triangle inequality in Illustrative Mathematics Grade 5?
Classifying triangles by side lengths and the triangle inequality theorem is covered in Chapter 7 of Illustrative Mathematics Grade 5, titled Shapes on the Coordinate Plane.
Can sides of 2 cm, 3 cm, and 7 cm form a triangle?
No. Check: 2 + 3 = 5, which is not greater than 7. The two shorter sides cannot bridge the gap to complete the triangle. The sides would fall flat rather than forming a closed shape.
What is a real-world illustration of the triangle inequality?
Imagine three sticks. If two short sticks combined are not long enough to reach across the gap between their ends when you lay the long stick down, they cannot form a triangle. The two shorter sticks must together exceed the longest stick's length.