Geometry and measures worksheet — GCSE Foundation

1.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.

2.A triangular prism has two triangular end faces and three rectangular faces joining them. How many faces does it have in total?

3.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.

4.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.

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

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

7.In triangle PQR and triangle STU, PQ = ST, QR = TU and PR = SU. Write down the congruence condition that proves the two triangles are congruent.

8.Work out the distance between the point (0, 0) and the point (5, 12).

9.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?

10.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

11.A quadrilateral has exactly two lines of symmetry, its two pairs of opposite angles are equal, and its diagonals are not equal in length. Write down the name of this quadrilateral.

12.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.

13.A furniture catalogue drawing uses a scale of 1 cm to 1.5 m. A sofa in the drawing is measured as 7 cm long. What is the real length of the sofa, in metres?

14.Work out the distance between the points (−3, 4) and (5, −2).

15.In triangle ABC, point D lies on side AB and point E lies on side AC, so that DE is parallel to BC. AD = 3 cm, DB = 6 cm and DE = 4 cm. Work out the length of BC.