Geometry and measures worksheet — GCSE Foundation

1.Write down the name given to a triangle whose three sides are all the same length.

2.A triangular bunting flag has two equal sides. The angle between those two equal sides is 80°, and the other two angles of the flag are equal to each other. Work out the size of each of the two equal angles.

3.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.

4.Point M lies exactly halfway between point A and point B, with A, M and B all on the same straight line. Which term correctly describes point M?

5.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.

6.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.

7.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

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

9.A roof truss is shaped like an isosceles triangle resting on a horizontal ceiling joist. The truss's sloping edges are equal in length, and the angle at its apex is 40°. The ceiling joist continues in a straight line beyond the foot of the truss. Work out the angle between the truss's sloping edge and the extended joist, on the outside of the truss.

10.A jug holds 750 ml of water. Work out what fraction of a litre this is.

11.A plan of a car park is drawn to a scale of 1 : 500. A parking bay is drawn as a rectangle measuring 1.2 cm by 0.6 cm. The real width of the bay corresponds to the 0.6 cm side. What is the real width of the bay, in metres?

12.A triangle has vertices A(1, 1), B(5, 1) and C(5, 4). Work out the lengths of AB, BC and CA, and write down whether triangle ABC is right-angled.

13.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?

14.Two straight lines cross at a point. To find the points that are the same distance from both lines, which construction should be used?

15.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?