Geometry and measures worksheet — GCSE Foundation

1.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.

2.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

3.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

4.A tent's sloping side makes an angle of 45° with the ground. The sloping side is 3√2 m long. Using the exact value of sin 45°, work out the exact height of the tent.

6.A line segment joins two points on the circumference of a circle, without necessarily passing through the centre. Write down the general term for this line segment.

7.Point A has coordinates (2, 5). Point A is translated to point B using the column vector with top number 6 and bottom number −3. Write down the coordinates of point B.

8.A regular polygon has 5 lines of symmetry. What is the order of rotational symmetry of this polygon?

9.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?

10.Write down the term for the distance all the way around the edge of a circle.

11.A builder props a straight plank against a vertical wall to reach a window ledge. The foot of the plank is 2.1 m from the base of the wall, and the plank is 3.5 m long. Work out how high up the wall the plank reaches.

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

13.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.

14.A tank holds 3.2 m³ of water. Work out this volume in litres.

15.A triangular badge has two sides of length 8 cm and a third side of length 5 cm. Work out the perimeter of the badge.