Foundation November 2023 Paper 1 Q23
23
(a) The measurements, in centimetres, of two triangles are shown in the table.
| Side 1 | Side 2 | Side 3 | |
|---|---|---|---|
| Triangle 1 | 2.5 | 3.2 | 4 |
| Triangle 2 | 7 | 8.96 | 11.2 |
Are the two triangles mathematically similar?
Show how you decide. [3]
(b) Are these two triangles definitely congruent?
Give a reason. [1]
Give a reason. [1]
Not to scale
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Three correct comparable ratios eg \(\frac{7}{2.5} = \frac{8.96}{3.2} = \frac{11.2}{4} = 2.8\) or two correct calculations eg \(\frac{3.2}{2.5} \times 7 = 8.96\) and \(\frac{4}{2.5} \times 7 = 11.2\) | M2 | M1 for 2 comparable ratios or for one correct calculation | 3 marks for 3 sides (6 values connected), “yes” and reason M2 for 3 sides (6 values connected) M1 for 2 sides (4 values connected) |
| Yes, the ratios are the same or Yes, the lengths are correct | 1dep | dependent on M2 scored | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| No, length of sides is not known | 1 | Allow BOD for No, with a justifiable mathematical reason in relation to the diagram, e.g. angles in a triangle add to \(180^\circ\) | |