Geometry and measures worksheet — GCSE Foundation

1.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.

2.A locus is described as the set of points exactly 4 cm from a fixed point O. What shape is this locus?

3.A tangent to a circle with centre O touches the circle at point P, where OP = 5 cm. Point Q lies on the tangent so that PQ = 12 cm. Using the fact that a tangent is perpendicular to the radius at the point of contact, work out the length OQ.

4.A conservatory has a roof panel shaped like a regular octagon. Work out the interior angle of the octagon, then use it to work out the size of the reflex angle at the same vertex, on the outside of the roof panel.

5.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

6.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

7.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.

8.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.

9.The diagram shows a solid built from identical cubes. How many squares are in its plan view, the view looking straight down from above?

10.A patio plan states: 'Side AB of the patio is parallel to side DC, and AB is longer than DC. Sides BC and AD are not parallel to each other and are not equal in length.' The four sides measure AB = 5.1 m, BC = 3.2 m, DC = 2.8 m and AD = 4.5 m. The tiler needs to order edging strip only for the sides that are not parallel to any other side. What total length of edging strip, in metres, should the tiler order?

11.Which of these describes an obtuse angle?

12.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

13.A solid is built from centimetre cubes standing on a table. Seen from the front, the left-hand column is 2 cubes high, the middle column is 2 cubes high and the right-hand column is 1 cube high. Work out how many squares make up the front elevation.

14.Triangle ABC has AB = 6 cm, BC = 8 cm and angle B = 90°. Triangle XYZ has XY = 6 cm, YZ = 8 cm and angle Y = 90°. Which congruence statement correctly shows the matching vertices?

15.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.