Geometry and measures worksheet — GCSE Foundation

1.An angle is measured with a protractor as 47°. What type of angle is this?

2.Write down the column vector that describes a translation of 5 units to the left and 3 units down.

3.A solid cube has a volume of 8 cm³. Work out the length of one edge of the cube.

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

5.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

6.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.

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

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

10.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?

11.In triangle ABC, point D lies on side AB and point E lies on side AC, so that DE is parallel to BC. AD = 3 cm, DB = 6 cm and DE = 4 cm. Work out the length of BC.

12.Lines JK and LM are parallel. A straight line crosses JK at point P and crosses LM at point Q. Angle KPQ = 118°. Angle KPQ and angle MQP are co-interior (allied) angles. Work out angle MQP.

13.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?

14.A regular hexagon is divided into six identical triangles by joining its centre to each of the six vertices. Work out the size of the angle of one of these triangles at the centre of the hexagon.

15.In triangle ABC and triangle DEF, AB = DE, AC = DF, and the angle at A equals the angle at D. Write down the congruence condition that proves the two triangles are congruent.