Geometry and measures worksheet — GCSE Foundation

1.Triangles LMN and XYZ have LM = XY, MN = YZ and LN = XZ. Give a reason why triangle LMN is congruent to triangle XYZ.

2.Lines PQ and RS are parallel. A straight line crosses PQ at point X and crosses RS at point Y. Angle PXY = 63°. Angle PXY and angle XYS are co-interior (allied) angles, which add up to 180°. Work out the size of angle XYS.

3.Which of the following correctly describes what it means for two lines to be perpendicular?

4.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.

5.A ship sails 12 km on a bearing of 070° from a harbour to a buoy. It then sails a further 9 km, still on a bearing of 070°, from the buoy to a lighthouse. How far is the lighthouse from the harbour, in kilometres?

6.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?

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

8.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.

9.Which of the following is NOT one of the four basic conditions used to prove two triangles are congruent?

10.A solid is a single cube. Its plan view (from above), front elevation (from the front) and side elevation (from the side) are drawn separately. What shape is each of these three views?

11.Triangles ABE and CDE share the vertex E, where lines AC and BD cross at E. AE equals CE, and BE equals DE. Angle AEB and angle CED are formed as vertically opposite angles where the lines cross. Which condition proves that triangle ABE is congruent to triangle CDE?

12.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.

13.In triangle ABC and triangle DEF, the angle at A and the angle at D are both 40°, and the angle at B and the angle at E are both 70°. No side lengths are given. Write down whether the two triangles must be similar, with the reason.

14.Quadrilateral WXYZ has WX parallel to ZY, and WZ = XY (the two non-parallel sides are equal in length). Give a reason why angle W = angle X.

15.Write down the exact value of sin 45°.