Geometry and measures worksheet — GCSE Foundation

1.Triangle ABC has a right angle at B. Triangle DEF has a right angle at E. The hypotenuse of triangle ABC equals the hypotenuse of triangle DEF, and side AB equals side DE. Which condition proves that the two triangles are congruent?

2.A line segment joins two points on the circumference of a circle, without necessarily passing through the centre. Write down the general term for this line segment.

3.A roof truss is shaped like an isosceles triangle resting on a horizontal ceiling joist. The truss's sloping edges are equal in length, and the angle at its apex is 40°. The ceiling joist continues in a straight line beyond the foot of the truss. Work out the angle between the truss's sloping edge and the extended joist, on the outside of the truss.

4.A picture frame is a rhombus with a diagonal of 16 cm and a diagonal of 12 cm. The two diagonals meet at right angles at their midpoints. Work out the length of one side of the rhombus.

5.The diagram shows a prism resting on a table. Which shape is its front elevation, the view looking at it from directly in front?

6.Triangle ABC has AB = (2x + 3) cm, BC = 11 cm and angle B = 90°. Triangle DEF has DE = 13 cm, EF = 11 cm and angle E = 90°. Given that the two triangles are congruent by SAS, work out the value of x.

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

8.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.

10.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.

11.The diagram shows a solid made from two cuboids joined together. Which shape is the front elevation of this solid?

12.A shop sells a scale model of a van. The model and the real van are similar shapes, with lengths in the ratio 1 : 24. The model is 18.5 cm long. Work out the length of the real van, giving your answer in metres.

13.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.

14.A solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.

15.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.