O-LevelMathematicsGeometry4024/11 · Oct/Nov 2015 · Q256 Marks

ABCD is a parallelogram. BEF and CDF are straight lines. AB = 4 cm, DF = 2 cm and AE = 5 cm. [Figure: Parallelogram ABCD, with point E on AD, F such that B-E-F and C-D-F are straight lines. Dimensions 4, 2, 5 labeled. Arrows indicate parallel lines.]

(a)Show that triangles ABE and CFB are similar. Give reasons for each of your statements.[2]
(b)Calculate BC.[2]
(c)Triangle DFE is also similar to triangle ABE. Given that the area of triangle DFE is x cm², find the area of ABCD in terms of x.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.

[2] (a) Two corresponding pairs of angles equated, with reasons, from BAE = FCB opp. angles of a parm. ABE =CFB alternate angles AÊB = CBF alternate angles
[2] B1 for any one pair, with correct reason
[2] (b) 7.5 oe
[2] M1 for BC/5 = 6/4 oe
[2] (c) 12x
[2] B1 for seeing 4x or 9x as ΔΑΒΕ or ABCF respectively

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