Problem preview

G-GMD.6 Warmup M2-040-A01-V01

Use triangle angle-side relationships and triangle inequality in mathematical and real-world problems.

Classify three lengths with the strict triangle inequality

Problem

Classify whether positive side lengths \(3\), \(4\), and \(5\) form a nondegenerate triangle.

Three candidate segments with positive lengths 3, 4, and 5; no triangle or inequality conclusion is shown.

Big Picture

What this problem is really about

For positive lengths, sorting reveals the one triangle-closure comparison that can fail. We’ll identify the longest segment, compare it with the sum of the other two, insist on a strict inequality, and interpret equality separately as a flattened boundary case rather than a nondegenerate triangle.

Answer choices

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Preview only

No; 3 + 4 = 5.

No; 3 + 4 < 5.

Yes; 3 + 4 > 5.

No; the three side lengths must be equal.

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Curriculum context

Course: Math II
Standard: G-GMD.6
Category: Geometry
Domain: Geometric Measurement and Dimension
Objective: Use triangle angle-side relationships and triangle inequality in mathematical and real-world problems.
Problem type: Classify three lengths with the strict triangle inequality