Geometry and measures worksheet — GCSE Foundation

1.Which of the following is NOT one of the four basic conditions used to prove two triangles are congruent?

2.A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. Work out its area.

3.A trapezium has parallel sides of 5 cm and 11 cm, and a perpendicular height of 4 cm. Work out the area of the trapezium.

4.In this question, a curved surface counts as a face. How many faces does a sphere have?

5.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.

6.Triangles ABE and CDE share the vertex E, where lines AC and BD cross at E. AE equals CE, and BE equals DE. Angle AEB and angle CED are formed as vertically opposite angles where the lines cross. Which condition proves that triangle ABE is congruent to triangle CDE?

7.Write down the exact value of sin 45°.

8.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.

9.Two similar triangles have lengths in the ratio 5 : 8. A side of the smaller triangle is 6.5 cm. Work out the length of the corresponding side of the larger triangle.

10.A ladder rests against a wall, making an angle of 60° with the ground. The ladder is 2 m long. Using the exact value of sin 60°, work out how high up the wall the ladder reaches, giving your answer in centimetres.

11.Write down the exact value of sin 60°.

12.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.

13.A locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.

14.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.

15.Two similar triangular tiles have lengths in the ratio 3 : 5. The longest side of the smaller tile is 9 cm. Work out the length of the longest side of the larger tile.