Geometry and measures worksheet — GCSE Foundation

1.In parallelogram ABCD the vertices are labelled in order round the shape, so angle A and angle B are at the two ends of the same side. Angle A is 70°. Work out the size of angle B.

2.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.

3.A sector of a circle is bounded by two straight edges and one curved edge. Write down the mathematical term for each of the two straight edges.

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

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

6.Point C is at (2, 3). It is rotated 90° clockwise about the origin. Work out the coordinates of the image of point C.

7.How many vertices does a cylinder have?

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.

9.A landscaper marks out two triangular flower beds using stakes and a tape measure. Bed 1 has two edges of 5 m and 7 m, meeting at a corner with a marked angle of 60° between them. Bed 2 has edges of 5 m and 7 m, meeting at a corner also marked at 60° between them. The landscaper wants to check the two beds will be exactly the same size and shape using only these three measurements. Which condition proves the two beds are congruent?

10.In triangle PQR and triangle STU, PQ = ST, QR = TU and PR = SU. Write down the congruence condition that proves the two triangles are congruent.

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

12.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.

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

14.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.

15.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.