Geometry and measures worksheet — GCSE Foundation

1.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.

2.Two metal window frames are checked before installation. Frame A has edges of 40 cm and 65 cm, with a marked angle of 35° at the far end of the 65 cm edge, away from where the two given edges meet. Frame B has matching edges of 40 cm and 65 cm, with a matching 35° angle in the same position. The fitter wants to know if these measurements alone guarantee the two frames are congruent. What should the fitter be told?

3.Vertex X of a triangle is at (−3, 5). After a translation, the image of X is at (2, −1). Write down the column vector of this translation.

4.Point M lies exactly halfway between point A and point B, with A, M and B all on the same straight line. Which term correctly describes point M?

5.A solid pyramid has a square base of side 10 cm and four identical triangular faces. Its apex is directly above the centre of the base, at a vertical height of 12 cm, and the slant height of each triangular face — the distance from the apex to the midpoint of a base edge — is 13 cm. Work out the total surface area of the pyramid.

6.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.

7.Write down the name given to a triangle whose three sides are all the same length.

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

9.A circular plate has a diameter of 20 cm. Work out the area of the plate. Use π = 3.14.

10.A tangent to a circle touches the circle at exactly one point, P. Work out the size of the angle between the tangent and the radius drawn to P.

11.A solid has 5 faces, 9 edges and 6 vertices. Two of its faces are triangles and the other three are rectangles. Which solid is it?

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

13.ABCD is an isosceles trapezium. The sides AB and DC are parallel, and the two sloping sides AD and BC are equal in length. Angle D is 112°. Work out the size of angle B.

14.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?

15.A quadrilateral has exactly two lines of symmetry, its two pairs of opposite angles are equal, and its diagonals are not equal in length. Write down the name of this quadrilateral.