PEAZIT Aha card
Go straight to resources ↓The third vertex must satisfy two distances
After drawing AB, locate C at the intersection of circles centered at A and B with radii AC and BC.
| Relation | Meaning |
|---|---|
| AB = 5 cm | Draw the fixed base first. |
| AC = 4 cm; BC = 3 cm | The circles encode both distance conditions for C. |
| 3 + 4 > 5 | The shorter sides together exceed the longest side. |
One worked example
- AB = 5 cmDraw the fixed base first.
- AC = 4 cm; BC = 3 cmThe circles encode both distance conditions for C.
- 3 + 4 > 5The shorter sides together exceed the longest side.
Watch out: For a nondegenerate triangle, every pair of sides must sum to more than the third. Equality is insufficient.
Goal, prerequisites and card origin
What you will learn: Understand SSS construction and recognize impossible triangles.
What you need first: A circle consists of points equally distant from its center.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
After drawing AB, locate C at the intersection of circles centered at A and B with radii AC and BC.