Geometry and measures worksheet — GCSE Foundation

1.A straight line crosses a pair of parallel lines. One of the co-interior (allied) angles is 118°. Work out the size of the other co-interior angle.

2.Priya says: 'To find the arc length of a sector, you divide the circumference by the angle in degrees.' Which statement about Priya's method is correct?

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

4.The diagram shows a solid made from two cuboids joined together. Which shape is the front elevation of this solid?

5.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.

6.Write down the name given to a quadrilateral with exactly one pair of parallel sides.

7.A designer enlarges a drawing of a model car for a poster. She first enlarges the drawing by a scale factor of 1.5, and then enlarges that result by a further scale factor of 2. On the original drawing, the position of a wheel relative to the front bumper is given by the column vector with top number 4 and bottom number −3, in centimetres. What is the corresponding column vector on the poster, in centimetres?

8.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

9.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.

10.A trapezium-shaped garden bed has parallel sides of 2.5 m and 4.5 m, and a perpendicular width of 3 m. A gardener wants to know the area of the bed before ordering topsoil. Work out the area of the garden bed.

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

12.A conservatory has a roof panel shaped like a regular octagon. Work out the interior angle of the octagon, then use it to work out the size of the reflex angle at the same vertex, on the outside of the roof panel.

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

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.Write down the exact value of tan 0°.