Geometry and measures worksheet — GCSE Foundation

1.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?

2.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.

3.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).

4.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.

5.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.

6.The diagram shows the plan view and the front elevation of a cuboid-shaped box, each drawn as a rectangle. Work out the area of the box's side elevation, in square centimetres.

7.Shape S has a vertex at (9, 6). It is enlarged by a scale factor of 1/3, centre the origin. Work out the coordinates of the image of this vertex.

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

9.Write down the number of lines of symmetry a rhombus has.

10.Point E is at (4, 2). It is rotated 180° about the point (1, 1). Work out the coordinates of the image of point E.

11.A regular nonagon has 9 sides. Work out the sum of its interior angles.

12.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.

13.An isosceles trapezium has exactly one pair of parallel sides, and its two non-parallel sides are equal in length. How many lines of symmetry does it have?

14.The column vector r has top number 2 and bottom number 6. Which of these column vectors is parallel to r?

15.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².