Foundation June 2025 Paper 1 Q16
16
\(AED\) and \(BCD\) are straight lines.
\(ED = EC\)
Show that \(EC\) is parallel to \(AB\).
Give a reason for each stage of your working. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| Shown | C1 | for angle \(ECD = 70\) or for angle \(ADB = 70\) and angle \(DAB = 40\) |
| C1 | for a correct relevant reason relating to finding an angle in a triangle, eg • base angles of an isosceles triangle are equal • sum of angles in a triangle is 180 | |
| C1 | for comparison of angles which would show that \(EC\) is parallel to \(AB\), eg • angle \(ECD\) = angle \(ABC\) (= 70) • angle \(BAD\) = angle \(CED\) (= 40) • angle \(BCX\) = angle \(ABC\) (= 70) • angle \(AEY\) = angle \(BAD\) (= 40) • angle \(ECB = 110\) and angle \(ECB\) + angle \(CBA = 180\) • angle \(AEC = 140\) and angle \(BAD\) + angle \(AEC = 180\) • angle \(ECD\) = angle \(ABD\) (= 70) and angle \(DAB\) = angle \(DEC\) (= 40) | |
| C1 | for a correct reason relating to angles in parallel lines which would show that \(EC\) is parallel to \(AB\), eg • corresponding angles are equal with angle \(ECD\) = angle \(ABC\) (= 70) • corresponding angles are equal with angle \(BAD\) = angle \(CED\) (= 40) • alternate angles are equal with angle \(BCX\) = angle \(ABC\) (= 70) • alternate angles are equal with angle \(AEY\) = angle \(BAD\) (= 40) • co-interior angles add to 180 with angle \(ECB\) + angle \(CBA = 180\) • co-interior angles add to 180 with angle \(BAD\) + angle \(AEC = 180\) • similar triangles with angle \(ECD\) = angle \(ABD\) (= 70) and angle \(DAB\) = angle \(DEC\) (= 40) |
Additional guidance
May be seen on the diagram
Do not award if an incorrect statement about angles in triangles seen.
Allow alternative correct labelling of angles eg angle \(ABD\) for angle \(ABC\)
Must be identified in some way, not just angles written on diagram.
Angles must be unambiguously identified.
Where \(X\) is a point on \(EC\) extended.
Where \(Y\) is a point on \(CE\) extended.
Reason must be consistent with their method.
If superfluous reasons seen then we need the correct appropriate reason to be linked to the comparison of angles.
Incorrect statement(s) seen is maximum 3 marks.
Accept allied for co-interior.