O-LevelMathematicsGeometry4024/12 · Oct/Nov 2021 · Q123 Marks
The diagram shows a rectangle ABCD. E is a point on the diagonal AC such that DÊC = 90°. Prove that triangle ADC is similar to triangle DEC. Give a reason for each statement you make. [Figure X.X]
- (a)Prove that triangle ADC is similar to triangle DEC. Give a reason for each statement you make.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [3] ACD = DCE, shared angle
- ADC = DÊC=90, [given]
- DAC = EDC [third] angles in a triangle
- Three angles equal, therefore the triangles are similar
- B2 for two correct pairs of angles with correct reasons or B1 for one correct pair of angles with correct reason or two correct pairs of angles with incorrect/no reasons
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