Higher November 2023 Paper 6 Q8
8 The diagram shows four triangles that are joined together.
Not to scale
- Points A, B, C and D lie on a straight line.
- Triangles ABF and CDE are equilateral triangles.
- Triangle BCF is an isosceles triangle with BF = BC.
Show that triangle CEF is a right-angled triangle.
Give a reason for each stage of your working.
Use the template below to help present your work. You may not need all of the lines.
Angle …… = ……° because ……
Angle …… = ……° because ……
Angle …… = ……° because ……
Angle …… = ……° because ……
Angle …… = ……° because ……
Angle …… = ……° because ……
Angle …… = ……° because …… [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| ABF 60 equilateral/all angles equal | 1 | If 0 or 1 scored, instead award SC2 for all of these angles correct in template or on diagram | Ignore other angles Accept in any order Condone spelling |
| FBC 120 straight line/line adds to 180 | 1 | ||
| BCF 30 isosceles/ BCF=BFC and angles in triangle add to 180 | 1 | If 0 scored, instead award SC1 for two of the first four angles correct in template or on diagram | |
| ECD 60 equilateral/all angles equal | 1 | For full marks, must be convinced they are working forwards and not backwards | |
| FCE 90 straight line and 180–30–60 | 1 | ||