Track quiz
Nine ideas, nine checks. The table comes first.
| Idea | How it goes |
|---|---|
| SAS | Two sides and the angle between them fix one triangle. |
| SSA | Two sides and another angle can give two triangles. |
| RHS | Right angle, hypotenuse and a leg fix one triangle. |
| AAS | Two angles give the third. Then it is ASA. |
| Equal sides | They give equal base angles. |
| Equal angles | They give equal sides. |
| Counter-example | One failing case ends a claim that says always. |
| Matching parts | Every matching side and angle must be equal. |
| Apex bisector | It halves the apex and the base. It meets the base at 90°. |
Sides 9 and 4 with 30° between them. How many triangles fit?
A 30° angle has 8 beside it and 5 opposite. How many triangles fit?
A right triangle has hypotenuse 10 and a leg of 6. How long is the third side?
Two angles are 72° and 47°. What is the third angle?
An isosceles triangle has base angles of 76°. What is the apex angle?
In triangle PQR, angle Q = angle R, and PQ = 8. How long is PR?
A claim about triangles passes 200 tries. One case fails. What does that case do to the claim?
One triangle has sides 5, 7, 9. Another has sides 9, 5, 7. Are they congruent?
Triangle ABC has AB = AC and a base BC of 12. Its apex bisector meets BC at D. How long is BD?
Next: 4-gons (Quadrilaterals). The same kind of reasoning, on four-sided figures.