Geometry and measures worksheet — GCSE Foundation

1.In a construction, a point P is marked at the foot of the perpendicular drawn from point X to a straight line. Which statement correctly compares the distance XP with the distance from X to any other point on the line?

2.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).

3.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.

4.Lines GH and JK are parallel. A straight line crosses GH at point M and crosses JK at point N. Angle HMN = 71°. Angle HMN and angle MNK are alternate angles. Work out angle MNK.

5.A perpendicular bisector is drawn through the midpoint of a line segment AB. Which set of points does this construction show?

6.A map has a scale of 1 : 20 000. The distance between two villages is 3.4 km in real life. How long is this distance on the map, in centimetres?

7.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.

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

9.A solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.

10.A hiker walks due west. What is the three-figure bearing for this direction?

11.Triangle ABC has a right angle at B, hypotenuse AC = 13 cm and AB = 5 cm. Triangle DEF has a right angle at E, hypotenuse DF = 13 cm and DE = 5 cm. Which condition proves the two triangles are congruent?

12.A cylindrical drum and a cuboid box are being wrapped for a display. A shop assistant wraps only the flat faces of each item, not any curved surface. How many flat faces in total does the assistant wrap across both items?

13.An angle is measured with a protractor as 47°. What type of angle is this?

14.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.

15.An ice cream is made from a cone of radius 3 cm and height 10 cm, topped with a hemisphere of the same radius sitting exactly on top of the cone. Work out the total volume of the ice cream. Use π = 3.14. Give your answer to the nearest whole number. Volume of a cone = 1/3 × πr²h. Volume of a sphere = 4/3 × πr³.