Geometry and measures worksheet — GCSE Foundation

1.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?

2.The three angles of a triangle are 10°, 58° and 112°. Write down the name that describes this triangle.

3.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

4.How many edges does a triangular prism have?

5.Which of the following correctly describes what it means for two lines to be perpendicular?

6.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

7.A straight transversal crosses a pair of parallel lines. At one crossing point, the angle between the transversal and a parallel line is 118°. Work out the size of the co-interior (allied) angle at the other crossing point.

8.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?

9.Shape S has an area of 48 cm². It is enlarged by a scale factor of 1/4 to give shape T. Work out the area of shape T.

10.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.

11.A surveyor is marking out field ABCD for a new crop. The plan states that side AB is parallel to side DC, but AB and DC are not equal in length, and sides BC and AD are not parallel to each other. Which term correctly describes the shape of field ABCD?

12.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

13.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?

14.A triangle has vertices A(1, 1), B(5, 1) and C(5, 4). Work out the lengths of AB, BC and CA, and write down whether triangle ABC is right-angled.

15.A ramp rises at 30° to the horizontal. Its sloping surface is 4.8 m long. Safety rules say the vertical rise of a ramp must be no more than 2.5 m. Work out how far below that limit the rise of this ramp is.