Higher November 2020 Unit 1 Q15
15. In the triangle \(EFH\) below:
- \(G\) is the midpoint of \(FH\),
- \(EG\) and \(FH\) are perpendicular.
Prove that \(EFG\) and \(EHG\) are congruent triangles.
You must state the condition of congruence. [4]
| Scheme | Marks | Comments |
|---|---|---|
| • FG = HG (since G is the midpoint of FH) | B1 | Do not accept indications on the diagram. |
| • EG is a common side | B1 | |
| • Angle EGF = Angle EGH (since EG and FH are perpendicular) | B1 | |
| SAS (or two sides and the included angle) so that EFG and EHG are congruent triangles. | B1 | FT from B2 previously awarded. Must be convincing. Do not allow ‘two sides and an angle’. |
Allow alternative method
| Scheme | Marks | Comments |
|---|---|---|
| • FG = HG (since G is the midpoint of FH) | B1 | Do not accept indications on the diagram. |
| • EG is a common side | B1 | |
| • EF = EH using Pythagoras | B1 | Must be convincing. An unsupported statement that EF = EH, or that triangle is ‘isosceles’, is insufficient. |
| SSS (or all corresponding sides equal) so that EFG and EHG are congruent triangles. | B1 | FT from B2 previously awarded. Allow RHS. Must be convincing. |