Geometry and measures worksheet — GCSE Foundation

1.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.

2.Shape S has a vertex at (9, 6). It is enlarged by a scale factor of 1/3, centre the origin. Work out the coordinates of the image of this vertex.

3.A solid has 6 faces: one pentagon and five triangles that all meet at a single point above the pentagon. What is the name of this solid?

4.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?

5.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.

6.A square tile has sides of length 6 cm. Work out the area of the tile.

7.A trapezium has parallel sides of 16 cm and 24 cm, and a perpendicular height of 7 cm. Work out the area of the trapezium.

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

9.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.

10.A trapezium-shaped garden bed has parallel sides of 2.5 m and 4.5 m, and a perpendicular width of 3 m. A gardener wants to know the area of the bed before ordering topsoil. Work out the area of the garden bed.

11.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

12.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.

13.Write down which one of these statements about quadrilaterals is true.

14.A parallelogram has a base of 20 cm and a sloping side of 13 cm. The perpendicular drawn from the top of that sloping side down to the base meets the base 5 cm from the foot of the sloping side, so the perpendicular, the 5 cm and the 13 cm sloping side form a right-angled triangle. Work out the area of the parallelogram.

15.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.