Higher June 2022 Paper 3 Q15
15 \(P\), \(Q\), \(R\) and \(S\) are four points on a circle.
\(PXR\) and \(SXQ\) are straight lines.
Prove that triangle \(PQX\) and triangle \(SRX\) are similar. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| Proof | C1 | for angle \(PQX\) = angle \(SRX\) as angles in the same segment are equal (or angles at the circumference subtended from the same arc/chord of a circle are equal) or angle \(QPX\) = angle \(RSX\) as angles in the same segment are equal (or angles at the circumference subtended from the same arc/chord of a circle are equal) or angle \(PXQ\) = angle \(SXR\) as vertically opposite angles/ vertically opposite angles are equal or for identifying two pairs of corresponding equal angles with no reason given |
| C1 | for identifying two pairs of corresponding equal angles with correct reasons given | |
| C1 | for stating that the triangles are similar because all three pairs of corresponding angles are equal with complete reasons given. |
Additional guidance
Underlined words need to be shown; reasons need to be linked to their method.
Could be shown on the diagram
Note that the students third/final reason may be: Angles in a triangle add up to 180