Geometry and measures worksheet — GCSE Foundation

1.Two angles lie on a straight line. One angle is 118°. Which reason correctly explains why the other angle is 62°?

2.How many vertices does a cuboid have?

3.A cuboid measures 5 cm long (left to right), 3 cm deep (front to back) and 2 cm tall. Its front elevation is 5 cm wide by 2 cm high. Its side elevation is 3 cm wide by 2 cm high. What are the dimensions of its plan view, looking down from above?

4.A garden water trough is a prism whose cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 120 cm long. Work out the volume of water needed to fill the trough completely.

5.In triangle ABC and triangle DEF, the angle at A and the angle at D are both 40°, and the angle at B and the angle at E are both 70°. No side lengths are given. Write down whether the two triangles must be similar, with the reason.

6.A straight line crosses two parallel lines. An angle of 65° is formed at one crossing. At the other crossing, the angle that lies between the two parallel lines on the opposite side of the crossing line is also 65°. Write down the angle fact that explains why these two angles are equal.

7.Each of these has an exact value. Write down the one whose value is the greatest.

8.Two similar triangles have lengths in the ratio 2 : 5. The sides of the smaller triangle are 4 cm, 6 cm and 8 cm. Work out the length of the longest side of the larger triangle.

9.A regular polygon has 5 lines of symmetry. What is the order of rotational symmetry of this polygon?

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

11.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

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

13.A bearing is described as being exactly halfway between north and east, measured clockwise. What is the three-figure bearing?

14.A ship's radio can be heard up to 30 km from the ship. A lighthouse's light can be seen up to 20 km from the lighthouse. The ship and the lighthouse are 40 km apart along the coast. Describe the region where BOTH the radio can be heard AND the light can be seen.

15.A circle is drawn on a page. Write down how many radii can be drawn in the circle.