Geometry and measures worksheet — GCSE Foundation

1.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.

2.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

3.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.

4.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.

5.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.

6.A sector of a circle has an angle of 150°. Work out what fraction of the circle's area the sector is.

7.Point D is at (3, 4). It is rotated 90° clockwise about the origin (0, 0). Work out the coordinates of the image of point D.

8.A roof truss is shaped like an isosceles triangle resting on a horizontal ceiling joist. The truss's sloping edges are equal in length, and the angle at its apex is 40°. The ceiling joist continues in a straight line beyond the foot of the truss. Work out the angle between the truss's sloping edge and the extended joist, on the outside of the truss.

9.Work out the exact value of sin 30° + cos 60°.

10.How many vertices does a cylinder have?

11.Two straight roads cross at a junction. The angle between them, measured with a protractor, is 118°. What is the size of the angle vertically opposite to it?

12.In triangle ABC the base BC is 10 cm long and the sloping side AB is 13 cm long. The perpendicular height from A down to BC is 12 cm. Work out the area of triangle ABC.

13.A parallelogram has an area of 136 cm² and a base of 17 cm. Work out the perpendicular height of the parallelogram.

14.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.

15.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.