Geometry and measures worksheet — GCSE Foundation

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

2.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

3.In triangle PQR and triangle STU, PQ = ST, QR = TU and PR = SU. Write down the congruence condition that proves the two triangles are congruent.

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 carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

6.Triangles PQS and RQS share the common side QS. PQ equals RQ, and PS equals RS. Which condition proves that triangle PQS is congruent to triangle RQS?

7.A map has a scale of 1 cm : 5 km. A road is drawn 3 cm long on the map. What is the real length of the road?

9.In a right-angled triangle, the side opposite angle θ is 6 cm and the hypotenuse is 10 cm. Work out the size of angle θ. Give your answer correct to 1 decimal place.

10.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.

11.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

12.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.

13.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.

14.Triangle ABC is extended so that side BC is extended beyond C to a point D, forming exterior angle ACD. Angle BAC = 48° and angle ABC = 67°. Which single angle fact gives angle ACD = 115° in one step, without first working out the interior angle at C?

15.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.