Geometry and measures worksheet — GCSE Foundation

1.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.

2.In a right-angled triangle one of the other two angles is 45°, and the side opposite that 45° angle is 7 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.

3.Two triangular offcuts of wood, PQR and STU, are cut for a construction project. PQ = 8 cm, QR = 6 cm and angle PQR = 90°. ST = 8 cm, TU = 6 cm and angle STU = 90°. A carpenter wants to check the two pieces are identical in shape and size before using them as a matching pair. Using only the measurements given, and without working out any further lengths, which condition proves that triangle PQR is congruent to triangle STU?

4.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?

5.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?

6.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?

7.The top of a clock tower is 25 m above level ground. Oliver stands on the ground 25 m from the foot of the tower. Work out the angle of elevation of the top of the tower from the point where Oliver stands.

8.A scale model of a bridge is built so that 2 cm on the model represents 5 m of the real bridge. The real bridge is 45 m long. Work out the length of the model bridge, in centimetres.

9.In triangle ABC and triangle DEF, the angle at A equals the angle at D, and AB ÷ DE = AC ÷ DF. Write down what this proves about the two triangles.

10.A trapezium has parallel sides of 5.6 cm and 8.4 cm, and a perpendicular height of 4 cm. Work out the area of the trapezium.

11.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.

12.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?

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

14.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.

15.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?