Geometry and measures worksheet — GCSE Foundation

1.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.

2.A stained-glass window panel is designed as a kite. Two adjacent sides are each 25 cm, and the other two adjacent sides are each 40 cm. A frame is fitted around the whole panel. The frame costs £2.50 per metre, sold only in whole metres. Work out the total cost of the frame.

3.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?

4.For two triangles to be proved congruent using SAS, which two facts must be true about both triangles?

5.Two similar flags have widths in the ratio 2 : 5. The width of the smaller flag is 8 cm. Work out the width of the larger flag.

6.Triangle ABC has a right angle at B. Triangle DEF has a right angle at E. The hypotenuse of triangle ABC equals the hypotenuse of triangle DEF, and side AB equals side DE. Which condition proves that the two triangles are congruent?

7.Shape S has a vertex at (9, 6). It is enlarged by a scale factor of 1/3, centre the origin. Work out the coordinates of the image of this vertex.

8.Write down the column vector that describes a translation of 5 units to the left and 3 units down.

9.A sign-maker is told a metal bracket outline must have two pairs of adjacent sides equal in length (not opposite pairs), exactly one pair of opposite angles equal, and exactly one line of symmetry. Which quadrilateral matches this description?

10.Triangle ABC has angle A = 40°, angle B = 65° and AB = 10 cm. Triangle DEF has angle D = 40°, angle E = 65° and DE = 10 cm. Which condition proves the two triangles are congruent?

11.The diagram shows a cuboid. Work out the area of its front elevation, in square centimetres.

12.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

13.In quadrilateral ABCD the two sides AB and BC are each 6 cm long and meet each other at B. The two sides CD and DA are each 9 cm long and meet each other at D. No side of ABCD is parallel to any other side. Write down the mathematical name of this quadrilateral.

14.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.

15.Point E is at (4, 2). It is rotated 180° about the point (1, 1). Work out the coordinates of the image of point E.