Geometry and measures worksheet — GCSE Foundation

1.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.

2.Triangle LMN has a right angle at M, with hypotenuse LN = 15 cm and LM = 9 cm. Triangle PQR has a right angle at Q, with hypotenuse PR = 15 cm and PQ = 9 cm. Which condition proves the two triangles are congruent?

3.A solid has 6 faces: one pentagon and five triangles that all meet at a single point above the pentagon. What is the name of this solid?

4.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?

5.A rhombus has all four sides equal in length. Which statement about a rhombus is correct?

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

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

8.Work out the exact value of (cos 45°)² + (sin 45°)².

9.Two similar shapes have lengths in the ratio 1 : 3. A side of the smaller shape is 4 cm long. Work out the length of the corresponding side of the larger shape.

10.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.

11.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?

12.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?

13.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.

14.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.

15.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.