Geometry and measures worksheet — GCSE Foundation

1.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.

2.A rectangular gate is braced with a diagonal strut. The gate is 1.2 m wide and 0.9 m tall. Work out the exact length of the diagonal strut.

3.Triangle ABC is right-angled at B. Triangle DEF is right-angled at E. AB = DE = 6 cm and AC = DF = 10 cm (AC and DF are the hypotenuses of their triangles). A student says this is not enough information to prove the triangles are congruent, because only two sides are given. Which reason shows the student is wrong?

4.Rectangle ABCD has vertices A(−1, 2), B(4, 2), C(4, 5) and D(−1, 5). The rectangle is translated so that C moves to (0, −1). Write down the coordinates of the image of A.

5.Two angles lie on a straight line. One angle is 118°. Which reason correctly explains why the other angle is 62°?

6.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.

7.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.

8.The angle between north and a cycle path is 40°, but it is measured anticlockwise from north. What is the three-figure bearing of the cycle path?

9.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?

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

11.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?

12.A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.

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

14.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

15.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.