Geometry and measures worksheet — GCSE Foundation

1.Write down the column vector that describes a translation of 4 units to the right and 4 units up.

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

3.A triangular prism has two triangular end faces and three rectangular faces joining them. How many faces does it have in total?

4.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

5.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

6.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.

7.How many edges does a triangular prism have?

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

9.A square-based pyramid is cut by a flat plane parallel to its base, partway up between the base and the apex. What shape is the cross-section?

10.A dog is tied by a lead 4 m long to a fixed ring on a straight garden wall. The wall extends much further than the lead can reach in both directions, and the dog cannot cross through it. Describe the region the dog can reach.

11.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

12.A straight fence is 5 m long. Describe the shape of the region made up of every point on the ground within 2 m of any part of the fence.

13.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).

15.A straight line crosses two parallel lines. An angle of 65° is formed at one crossing. At the other crossing, the angle that lies between the two parallel lines on the opposite side of the crossing line is also 65°. Write down the angle fact that explains why these two angles are equal.