Geometry and measures worksheet — GCSE Foundation

1.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?

2.A quadrilateral has all four sides equal in length and all four interior angles equal to 90°. Its diagonals are equal in length and bisect each other at right angles. Which quadrilateral matches this description exactly?

3.The perimeter of a square is 20 cm. Work out the area of the square.

4.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

5.A bus journey takes 2.5 hours. Work out how many minutes this is.

6.A path goes from A(1, 1) to B(1, 5), then from B to C(6, 5). Work out the total length of the path from A to C.

7.A sector of a circle has radius 8 cm and takes up three-quarters of the full circle. Work out the perimeter of the sector, in terms of π.

8.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.

9.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

10.A diameter divides a circle into two equal halves. Write down the special name given to each of these two halves.

11.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.

12.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?

13.A rectangle has vertices A(0, 0), B(6, 0), C(6, 4) and D(0, 4). Work out the length of the diagonal AC. Give your answer correct to 2 decimal places.

14.How many edges does a triangular prism have?

15.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder.