Geometry and measures worksheet — GCSE Foundation

1.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.

2.A triangular bunting flag has two equal sides. The angle between those two equal sides is 80°, and the other two angles of the flag are equal to each other. Work out the size of each of the two equal angles.

3.A builder lays a low wall made from identical bricks. The diagram shows the plan of the wall's footprint on a grid, where each square is one brick. The wall is built up to a height of 4 bricks everywhere. Work out the total number of bricks used.

4.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.

5.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.

6.A shop sells a scale model of a van. The model and the real van are similar shapes, with lengths in the ratio 1 : 24. The model is 18.5 cm long. Work out the length of the real van, giving your answer in metres.

7.A solid has 10 vertices and 15 edges. Using the formula F + V − E = 2, work out how many faces it has.

8.A solid has 4 triangular faces, 4 vertices and 6 edges. What is the name of this solid?

9.The diagram shows the plan of the base layer of a solid built from identical cubes. A second layer of cubes is added on top, filling the entire base layer to a height of 2 cubes everywhere. Work out how many squares are visible in the plan view of this solid.

10.Triangle ABC has AB = 8 cm, angle B = 50° and BC = 6 cm. Triangle DEF has DE = 8 cm, angle E = 50° and EF = 6 cm. Which condition proves the two triangles are congruent?

11.In the RHS congruence condition, which three facts must be true about two triangles for RHS to prove they are congruent?

12.Triangle ABC has angle A = 40°, angle B = 65° and AB = 10 cm. Triangle DEF has angle D = 40°, angle E = 65° and DE = 10 cm. Which condition proves the two triangles are congruent?

13.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?

14.The diagram shows a solid resting on its side on a table. Work out which shape is its plan view, the view looking straight down from above.

15.A transversal crosses a pair of parallel lines. At one line, the angle is (5x + 4)°. The corresponding angle at the other line is (3x + 24)°. Work out the value of x.