Geometry and measures worksheet — GCSE Foundation

1.A quadrilateral has both pairs of opposite sides parallel and equal in length, but none of its angles are right angles. Which statement about this quadrilateral is correct?

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

3.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.

4.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?

5.A locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.

6.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

7.A square-based pyramid has a square base and four identical triangular sloping faces, with its apex directly above the centre of the base. How many planes of symmetry does it have?

8.A sign-maker is told a metal bracket outline must have two pairs of adjacent sides equal in length (not opposite pairs), exactly one pair of opposite angles equal, and exactly one line of symmetry. Which quadrilateral matches this description?

9.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.

10.A regular hexagon is divided into six identical triangles by joining its centre to each of the six vertices. Work out the size of the angle of one of these triangles at the centre of the hexagon.

11.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?

12.A quadrilateral has two pairs of parallel sides. All four of its interior angles are right angles, but its sides are not all the same length. Which quadrilateral is this?

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

14.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

15.A tangent to a circle touches the circle at exactly one point, P. Work out the size of the angle between the tangent and the radius drawn to P.