Geometry and measures worksheet — GCSE Foundation

1.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

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

3.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

4.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

5.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.

6.A tank holds 3.2 m³ of water. Work out this volume in litres.

7.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

8.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).

9.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.

10.Which of the following is the correct definition of a regular polygon?

11.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.

12.A written description of a diagram states: 'AB is marked with a single arrow, CD is marked with a single arrow, and EF is marked with a double arrow.' Using the standard convention for marking parallel lines, what can be concluded?

13.A solid has two parallel, congruent polygon faces joined by flat rectangles, and its cross-section is the same shape all the way along its length. Which solid is it?

14.A quadrilateral has vertices A(1, 1), B(5, 1), C(6, 4) and D(2, 4). By comparing the y-coordinates of A, B and of D, C, write down whether the sides AB and DC are parallel, and give a reason for your answer.

15.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.