7th Grade · Geometry
Degenerate Triangle
7.G.A.2
Definition
Occurs when the sum of two sides equals the third side (a + b = c). The three points are collinear — the triangle collapses to a straight line with zero area.
Examples
- Sides 3, 4, 7: 3 + 4 = 7 — fails, collapses to a flat line.
- For a valid triangle, a + b must be strictly greater than c, not equal.
Key rule
Equal or less than the third side means degenerate or impossible.
Memory hook
Add up exactly right, and the triangle goes flat.