Geometry and measures worksheet — GCSE Foundation

1.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?

2.In triangle XYZ, the side opposite vertex X is labelled using the standard lowercase-letter convention. Which label is correct?

3.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

4.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?

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

6.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.

7.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.

8.A solid has two parallel, congruent polygon faces joined by flat rectangles, and its cross-section is the same shape all the way along its length. Which solid is it?

9.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?

10.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.

11.A bearing is described as being exactly halfway between north and east, measured clockwise. What is the three-figure bearing?

12.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?

13.A rhombus has all four sides equal in length. Which statement about a rhombus is correct?

14.Lines JK and LM are parallel. A straight line crosses JK at point P and crosses LM at point Q. Angle KPQ = 118°. Angle KPQ and angle MQP are co-interior (allied) angles. Work out angle MQP.

15.A circular table mat has diameter 20 cm. Yasmin has a 70 cm length of ribbon and sews it around the edge of the mat with no overlap. Using π = 3.14, work out how much ribbon is left over after going around the mat once.