Geometry and measures worksheet — GCSE Foundation

1.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.

2.A construction for the perpendicular bisector of AB begins by opening a pair of compasses to more than half the length of AB, then drawing an arc centred at A. What is the next step?

3.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.

4.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

5.Write down the exact value of cos 60°.

6.Triangle ABC and triangle DEF both contain a right angle, at B and E respectively, and the hypotenuses AC and DF are equal in length. Which extra fact would prove the triangles are congruent by RHS?

7.Write down the exact value of cos 45°.

8.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?

9.Work out the exact value of tan 30° + tan 30°.

10.A circle has a radius of 3 cm. Work out the diameter of the circle.

11.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.

12.A square has sides of length 7 cm. Work out its area.

13.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?

14.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.

15.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.