Higher November 2022 Paper 5 Q13
13 Points A, B, C and D lie on the circumference of a circle.
Line AC intersects line BD at point E.
Not to scale
Prove that triangle AED is similar to triangle BEC. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Angle AED = angle BEC and [vertically] opposite Angle DAE = angle EBC and same segment Angle ADE = angle ECB and same segment | M2 | For M2 only two of the three statements and reasons are required M1 for one pair of angles with a reason | Allow any unambiguous labelling for angles e.g. DAE or DAC or A, but not E For reason accept e.g. opp ∠’s For same segment, accept same arc but not same chord Accept 3rd angle in triangle oe for reason with final angle if other two given correctly with correct reasons |
| [Triangle AED is similar to triangle BEC] [corresponding] angles are equal oe or AAA oe OR After two pairs of angles with reasons gives 3rd pair of equal angles with a reason | A1 | With no errors or incorrect statements seen If 0 scored, SC1 for at least two correct pairs of angles identified with no / incorrect reasons | Accept they have the ‘same/equal angles’ oe, AA and similar. Accept symbol ~ for similar Condone angles identified on diagram for SC1 |