Geometry and measures worksheet — GCSE Foundation

1.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.

2.Triangle ABC has AB = 6 cm, BC = 8 cm and angle B = 90°. Triangle XYZ has XY = 6 cm, YZ = 8 cm and angle Y = 90°. Which congruence statement correctly shows the matching vertices?

3.Write down the column vector, from the options given, that would move a point to the right and downwards.

4.Triangle LMN has a right angle at M, with hypotenuse LN = 15 cm and LM = 9 cm. Triangle PQR has a right angle at Q, with hypotenuse PR = 15 cm and PQ = 9 cm. Which condition proves the two triangles are congruent?

5.A square-based pyramid has a square base and four identical triangular sloping faces, with its apex directly above the centre of the base. How many planes of symmetry does it have?

6.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.

7.ABCD is an isosceles trapezium. The sides AB and DC are parallel, and the two sloping sides AD and BC are equal in length. Angle D is 112°. Work out the size of angle B.

8.In quadrilateral ABCD, side AB is parallel to side DC. Which statement correctly uses geometric notation to show this?

9.Lines GH and JK are parallel. A straight line crosses GH at point M and crosses JK at point N. Angle HMN = 71°. Angle HMN and angle MNK are alternate angles. Work out angle MNK.

10.The diagram shows the plan, front elevation and side elevation of a solid. Which of these solids matches all three views?

11.A wooden block is a cuboid measuring 2 cm by 10 cm by 15 cm. Work out the volume of the block.

12.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.

13.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

14.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

15.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.