Higher June 2025 Paper 1 Q8
8 \(ABC\) is a right-angled triangle.
\(AEC\) and \(ADB\) are straight lines.
\(ED\) is parallel to \(CB\).
(a) Prove that triangle \(ABC\) is similar to triangle \(ADE\). (2)
\(ED = 20\) cm \(CB = 30\) cm \(AC = 18\) cm
(b) Work out the length of \(EC\). (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| Proof | M1 | for identifying angle \(A\) as common or for angle \(AED\) = angle \(ACB\) or angle \(ADE\) = angle \(ABC\) with appropriate reason(s) eg corresponding angles are equal or co-interior angles add up to 180 and angles on a straight line add up to 180 |
| C1 | for completing the proof by identifying a second pair of equal angles with appropriate reason(s) and a statement that the angles in each triangle are the same |
Additional guidance
Statement can be implied by identifying a third pair of equal angles (no reason needed)
| Answer | Mark | Mark scheme |
|---|---|---|
| 6 | P1 | for a scale factor of 1.5 or \(\dfrac{2}{3}\) oe or for \(\dfrac{AE}{20} = \dfrac{18}{30}\) oe |
| P1 | for a process to find the length of \(AE\), eg \(18 \div 1.5\ (= 12)\) oe or \((AE =)\ \dfrac{20 \times 18}{30}\) oe or for a complete process to find the length of \(EC\), eg \(18 \times \left(1 - \dfrac{2}{3}\right)\) oe | |
| A1 | cao |