Testing Triangle Inequality On ASVAB Triples

This animation checks whether four common length sets—3-4-5, 5-12-13, 7-24-25, and 8-15-17—can form triangles by applying the triangle inequality theorem: the sum of any two sides must exceed the third. Each set is tested visually, showing sides joining to close a triangle. These same sets are also right triangle Pythagorean triples, a pattern frequently tested on the ASVAB. Useful for students preparing for military entrance exams or reviewing basic geometry rules about valid triangle formation.

Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy

The prompt that made it

Which set of lengths can form a triangle? Talk about these four lengths that usually appear on the Asvab: 3–4–5 5–12–13 7–24–25 8–15–17 Audience: 13-19

Make your own version

Make the next one in this series

• Show why these same four triples also satisfy the Pythagorean theorem
• Animate what happens when a length set fails the triangle inequality test
• Compare triangle inequality with the law of cosines for non-right triangles