Printable · GCSE Foundation · ages 14-16
Properties of triangles and quadrilaterals worksheet — GCSE Foundation
Fifteen questions on "properties of triangles and quadrilaterals" — DfE statement G4. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
Properties of triangles and quadrilaterals worksheet — GCSE Foundation
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- 1.Two sides of a triangle are 9 cm and 15 cm long. Write down which one of these lengths is possible for the third side.
- 2.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.
- 3.In parallelogram ABCD the vertices are labelled in order round the shape, so angle A and angle B are at the two ends of the same side. Angle A is 70°. Work out the size of angle B.
- 4.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.
- 5.Quadrilateral PQRS has angle P = 92°, angle Q = 84° and angle R = 106°. Work out the size of angle S.
- 6.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.
- 7.A garden bed is designed as a trapezium. The two parallel sides are 8 m and 12 m, and the perpendicular distance between them is 5 m. Grass seed covers 4 m² per bag, sold only in whole bags. Work out how many bags of grass seed are needed.
- 8.A tile is described as having two pairs of parallel sides, four equal sides, and diagonals that cross at right angles but are not equal in length. Give a reason why this tile cannot be a square.
- 9.Quadrilateral WXYZ has WX parallel to ZY, and WZ = XY (the two non-parallel sides are equal in length). Give a reason why angle W = angle X.
- 10.In kite WXYZ, WX = WZ and XY = ZY (so at each of X and Z, one side from each of the two unequal pairs meets). Angle X = 100°. Work out angle Z.
- 11.Write down the number of lines of symmetry a rhombus has.
- 12.Write down how many right angles a rectangle has.
- 13.Write down the name given to a quadrilateral that has exactly one pair of parallel sides.
- 14.In a kite, one pair of opposite angles are equal in size. In kite WXYZ, angle X = 40° and angle Z = 100° are the two angles that are NOT equal to each other. The other two angles, W and Y, are equal to each other. Work out the size of angle W.
- 15.In an isosceles triangle each of the two base angles is 46°. Work out the size of the angle at the apex.
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