O-LevelMathematicsGeometry4024/11 · Oct/Nov 2021 · Q225 Marks
ACD and BCE are straight lines. AB is parallel to ED. [Figure with two triangles ABC and DEC, where A,C,D are collinear and B,C,E are collinear, and AB || ED]
- (a)Prove that triangle ABC is similar to triangle DEC. Give a reason for each statement that you make.[3]
- (b)AB = 6 cm and ED = 2 cm. The area of triangle ABC is 45 cm². Calculate the area of triangle DEC.[2]
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.
- 22(a) ∠ACB = ∠ECD [vertically] opposite ∠CAB = ∠CDE alternate ∠ABC = ∠CED alternate Three angles equal therefore the triangles are similar [3] 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
- 22(b) 5 cm² [2] B1 for (2/6)² oe or (1/3)² oe soi
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