Geometry and measures worksheet — GCSE Foundation

1.An angle measures 108°. Write down the name given to an angle of this size.

2.A regular polygon has 5 lines of symmetry. What is the order of rotational symmetry of this polygon?

3.A solid is a single cube. Its plan view (from above), front elevation (from the front) and side elevation (from the side) are drawn separately. What shape is each of these three views?

4.A square-based pyramid is cut by a flat plane parallel to its base, partway up between the base and the apex. What shape is the cross-section?

5.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.

6.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

7.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.

8.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.

9.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.

10.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.

11.A rhombus has all four sides equal in length, but it is not a square — its angles are not all 90°. How many lines of symmetry does this rhombus have?

12.In a kite, one pair of opposite angles are equal in size. In kite WXYZ, angle X = 40° and angle Z = 100° are the two angles that are NOT equal to each other. The other two angles, W and Y, are equal to each other. Work out the size of angle W.

13.Work out the exact value of (cos 45°)² + (sin 45°)².

14.Two similar triangles have lengths in the ratio 5 : 8. A side of the smaller triangle is 6.5 cm. Work out the length of the corresponding side of the larger triangle.

15.In parallelogram ABCD the vertices are labelled in order round the shape, so angle A and angle B are at the two ends of the same side. Angle A is 70°. Work out the size of angle B.