Higher June 2018 Paper 1 Q10
10.
Diagram not drawn to scale
The diagram shows a triangle BDF.
The straight lines CE and ABF are parallel.
Prove that \(w = x + y\).
Give a reason for each statement you make in your proof. [3]
| Scheme | Marks | Comments |
|---|---|---|
| Two correct angles or \(x + y + DCE = 180\) (Angles in a triangle (sum to 180°)) \(DCE = DBF\) (Corresponding angles (are equal)) \(w + DBF = 180\) (Angles on a straight line (sum to 180°)) | B1 | May be shown on diagram; angles need to be indicated in some way Angle DFB = \(y\) or Angle DFA = \(y\) (Corresponding angles (are equal)) and Angle DBF = 180 − \(x - y\) (Corresponding angles (are equal) or Angles in a triangle (sum to 180°)) or Angle DCE = 180 − \(x - y\) (Angles in a triangle (sum to 180°)) or Angle DCE = 180 − \(w\) (Corresponding angles (are equal)) and Angle DBF = 180 − \(x - y\) (Corresponding angles (are equal) or Angles in a triangle (sum to 180°)) or Angle DBF = 180 − \(w\) (Angles on a straight line (sum to 180°)) |
| A correct reason linked to a correct statement | B1 | |
| Fully correct and justified complete argument to prove \(w = x + y\) | B1 | Must be fully justified with all valid reasons |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Angle DFB = \(y\) or Angle DFA = \(y\) Corresponding angles are equal or angle BCE = \(w\) alternate angle are equal | B1 | |
| \(w = x + y\) The exterior angle is equal to the sum of the two opposite interior angles | B2 |
| (3) |
Corrected by Westie's Workshop
- The board's mark scheme printed “(Corresponding angles (are equal)”. Changed to “(Corresponding angles (are equal))” because a closing bracket was missing.
Original: see the board's mark scheme PDF (link above).