Higher June 2017 Paper 2 Q15
15 \(A\), \(B\), \(C\) and \(D\) are four points on the circumference of a circle.
\(AEC\) and \(BED\) are straight lines.
Prove that triangle \(ABE\) and triangle \(DCE\) are similar.
You must give reasons for each stage of your working. (3)
| Answer | Mark | Notes |
|---|---|---|
| Proof | C1 | for identifying one pair of equal angles with a correct reason, e.g. (angle) \(BAE\) = (angle) \(CDE\); angles in the same segment are equal or angles at the circumference subtended on the same arc are equal or for identifying two pairs of equal angles with no correct reasons given (angles must be within the appropriate triangles) |
| C1 | for identifying a second pair of equal angles with a correct reason, e.g. (angle) \(AEB\) = (angle) \(DEC\); opposite angles or vertically opposite angles are equal or for identifying the three pairs of equal angles with no correct reasons given | |
| C1 | for stating the three pairs of equal angles of the two triangles e.g. \(ABE = DCE\), \(BEA = CED\), \(EAB = EDC\) with fully correct reasons |