O-LevelMathematicsGeometry4024/21 · May/June 2024 · Q35 Marks

Triangle PQR is isosceles with PQ = QR. The exterior angle of the triangle at R is 142°. Calculate angle PQR. Angle PQR =

(a)Triangle PQR is isosceles with PQ = QR. The exterior angle of the triangle at R is 142°. Calculate angle PQR. Angle PQR =[2]
(b)The diagonals of trapezium ABCD meet at E. Show that triangle ABE is similar to triangle CDE. Give a reason for each statement you make.[3]

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Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

[2] 104
[2] B1 for angle QRP = 38 or angle QPR = 38
[2] or M1 for 180-2×their 38
[3] angle AEB = angle CED [vertically] opposite angles
[3] angle EAB = angle ECD alternate angles
[3] angle EBA = angle EDC alternate angles
[3] or angles in a triangle add to 180 as reason for the third pair
[3] Hence similar
[3] B2 for two correct pairs of angles with correct reasons
[3] or B1 for one correct pair of angles with correct reason or two correct pairs of angles with no/incorrect reasons

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