The big picture
One question matters most here. How many triangles fit these measurements?
| Idea | Remember | Example |
|---|---|---|
| SAS | Two sides and the angle between fix one triangle. | 7, 55°, 5 |
| SSA | Two sides and another angle can give two triangles. | 30°, 8, 5 gives two |
| RHS | Right angle, hypotenuse and a leg fix one triangle. | 13 and 5 give 12 |
| AAS | Two angles give the third. Then it is ASA. | 70° and 60° give 50° |
| Equal sides | They give equal base angles. | Apex 40°, base 70° each |
| Equal angles | They give equal sides. | Base angles 70°, sides equal |
| Counter-example | One failing case ends a claim that says always. | 30°, 8, 5: not always one |
| Matching parts | Every matching side and angle must be equal. | 6, 8, 10 and 9, 12, 15 differ |
| Apex bisector | It halves the apex and the base. It meets the base at 90°. | Base 10 gives pieces of 5 |
One triangle can be drawn many ways. Turning or flipping a triangle changes how it looks, not the triangle.