Higher November 2016 Unit 1 Q16
16. Triangle ABC is an isosceles triangle with \(A\hat{B}C = A\hat{C}B\).
Diagram not drawn to scale
P and Q are points on AB and AC respectively such that AP = AQ.
Prove that triangle ABQ is congruent to triangle ACP.
You must give reasons for each step of your proof. [4]
| Scheme | Marks | Comments |
|---|---|---|
| AB = AC because ABC is an isosceles triangle. | B2 | B1 for AB = AC alone. |
| AP = AQ AND angle  common. | B1 | |
| (So triangles ABQ and ACP are congruent because of) ‘two sides and the included angle’ or ‘SAS’. | B1 |