O-LevelMathematicsGeometry4024/12 · May/June 2022 · Q174 Marks
Ryan says: Each diagonal of quadrilateral Q divides it into two congruent isosceles triangles. Draw a ring around each of the quadrilaterals in the list for which Ryan's statement is always true. Square Rectangle Rhombus Parallelogram Trapezium Kite
- (a)Ryan says: Each diagonal of quadrilateral Q divides it into two congruent isosceles triangles. Draw a ring around each of the quadrilaterals in the list for which Ryan's statement is always true. Square Rectangle Rhombus Parallelogram Trapezium Kite[1]
- (b)[Figure showing two intersecting lines AXB and CXD forming triangles AXC and BXD] AXB and CXD are straight lines. X is the midpoint of AB. AC is parallel to DB. Show that triangle AXC is congruent to triangle BXD. 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 (May/June 2022). The mark or mark type is shown in brackets.
- [1] (a) Square Rhombus
- [3] (b) Two correct pairs of angles from ∠AXC = ∠BXD, ∠CAX= ∠DBX and ∠ACX= ∠BDX with correct reasons and AX = BX with correct reason and ASA stated e.g. AX = BX given ∠AXC = ∠BXD [vertically] opposite ∠CAX= ∠DBX alternate [angles] [Congruent] ASA B2 for two pairs of equal sides/angles with correct reasons or B1 for one pair of equal sides/angles with correct reason or for two appropriate pairs with no or incorrect reasons
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