Geometry and measures worksheet — GCSE Foundation

1.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.

2.In triangle ABC and triangle DEF, the angle at A equals the angle at D, and AB ÷ DE = AC ÷ DF. Write down what this proves about the two triangles.

3.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.

4.Two similar flags have widths in the ratio 2 : 5. The width of the smaller flag is 8 cm. Work out the width of the larger flag.

5.In kite WXYZ, WX = WZ and XY = ZY (so at each of X and Z, one side from each of the two unequal pairs meets). Angle X = 100°. Work out angle Z.

6.A triangle has vertices A(1, 1), B(5, 1) and C(5, 4). Work out the lengths of AB, BC and CA, and write down whether triangle ABC is right-angled.

7.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

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

9.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.

10.A ladder rests against a wall, making an angle of 60° with the ground. The ladder is 2 m long. Using the exact value of sin 60°, work out how high up the wall the ladder reaches, giving your answer in centimetres.

11.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?

12.Two triangles are congruent to each other. What does this tell you about their angles and sides?

13.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.

14.A solid pyramid has a square base of side 6 cm. Its apex is directly above the centre of the base, at a vertical height of 8 cm. Work out the volume of the pyramid.

15.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.