Higher November 2024 Paper 2 Q24
24 In the diagram,
\(ABCD\) and \(AEFG\) are congruent rectangles
\(D\) lies on \(EF\)
angle \(ADE = x\)
Not drawn accurately
Prove that \(GD\) bisects angle \(ADF\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Response showing that \(GD\) bisects angle \(ADF\) and all reasons | B4 | B3 response showing that \(GD\) bisects angle \(ADF\) B2 correct expressions for two angles in terms of \(x\) (angles must be above \(AD\)) or two correct statements about a pair of angles (angles must be above \(AD\)) B1 correct expression for one angle in terms of \(x\) (angle must be above \(AD\)) or one correct statement about a pair of angles (angles must be above \(AD\)) |
Additional guidance
Correct expressions for angles (which may be seen on the diagram) include
angle \(DAG = x\)
angle \(ADF = 180 - x\)
angle \(ADG = \dfrac{180 - x}{2}\) or \(90 - \dfrac{x}{2}\)
angle \(AGD = \dfrac{180 - x}{2}\) or \(90 - \dfrac{x}{2}\)
angle \(GDF = 180 - x - \dfrac{180 - x}{2}\) or \(\dfrac{180 - x}{2}\) or \(90 - \dfrac{x}{2}\)
angle \(DGF = \dfrac{x}{2}\)
Expressions must be explicit eg do not accept angle \(ADF + x = 180\) unless recovered
Correct statements about a pair of angles include
angle \(AGD\) = angle \(GDF\)
angle \(AGD\) = angle \(ADG\)
angle \(ADG\) = angle \(GDF\)
angle \(AGD = 90 -\) angle \(DGF\)
angle \(GDF = 90 -\) angle \(DGF\)
Accept eg angle \(AGD\) and angle \(ADG\) both labelled \(y\) as a correct statement about a pair of angles
Accept eg \(\widehat{DAG}\) for angle \(DAG\)
Do not accept a single upper case letter for an angle unless shown on the diagram
For up to B2 allow assumption that \(GD\) bisects angle \(ADF\)
Reasons needed will depend on the approach used and will include some of
alternate angles (are equal)
(base) angles of isosceles triangle (are equal)
angles in rectangle are 90
angles of triangle (add up to 180)
(adjacent) angles on a (straight) line (add to 180)