Foundation June 2017 Paper 2 Q21
21 Triangles P and Q are right-angled.
Not to scale
(a) Show that the two shorter sides in triangle P have the same lengths as the two shorter sides in triangle Q. [3]
(b) Explain why the two triangles are congruent. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(13^2 - 12^2\) or \(169 - 144\) | M1 | Or \(5^2 + 12^2\) or \(25 + 144\) | \(5^2 + 12^2\) seen with \(13^2 + 12^2\) scores M0 May be seen in stages eg \(5 \times 5 = 25\) \(12 \times 12 = 144\) \(25 + 144 =\) |
| \(\sqrt{13^2 - 12^2}\) soi | M1 dep | or \(\sqrt{5^2 + 12^2}\) soi | For second M1 must see \(\sqrt{\phantom{x}}\) symbol \(\sqrt{13^2 + 12^2}\) scores M0 |
| Two shortest sides in both triangles are 5 [cm] and 12 [cm] | A1 | or 5[cm] side clearly labelled on triangle P and 13[cm] clearly labelled on triangle Q | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [All] the sides are the same length | 1 | Accept SAS or RHS or SSS soi | See Appendix B |
Appendix B
Exemplar responses for Q21(b)
| Response | Mark |
|---|---|
| Their sides are the same lengths | 1 |
| They both have the same side lengths and are right angled | 1 |
| EXACTLY the same – angles and sides | 1 |
| They both has a right angles with the adjacent side being 12cm and their hypotenuse be 13cm | 1 |
| The measurements of their sides have not changed only the position of the shape has same implied | 1 |
| Because they’re both a right angle triangles with the same length lines | 1 |
| Same lengths on each line | 1 |
| Same lengths and angles | 1 |
| Because they are both right angle triangles with the same lengths | 1 |
| Because they both have the same sides | 1 |
| The two triangles are congruent as they have same sides and shape | 1 |
| RHS sometimes this is implied from a worded sentence | 1 |
| They have the same measurements exactly measurements could refer to angles | 0 |
| Because they are the same size and do not change shape. Sides not referred to | 0 |
| As they both have the same numbers and a right angle | 0 |
| Two sides have the same length | 0 |
| Because they both have the same length short side and are both right angled triangles ‘Short sides’ would imply SAS and so score 1 | 0 |
| Because they have 2 sides and an angle that are the same ‘and angle inbetween’ would score 1 | 0 |
| They are the same but just at a different position | 0 |
| ASA | 0 |