Geometry and measures worksheet — GCSE Foundation

1.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.

2.Triangle ABC is translated by the column vector with top number 3 and bottom number −5 to form triangle A′B′C′. Triangle A′B′C′ is then translated by the column vector with top number −7 and bottom number 2 to form triangle A″B″C″. Work out the single column vector that translates triangle ABC directly to triangle A″B″C″.

3.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.

4.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.

5.An angle is measured with a protractor as 47°. What type of angle is this?

6.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

7.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.

8.A rectangle has vertices A(0, 0), B(6, 0), C(6, 4) and D(0, 4). Work out the length of the diagonal AC. Give your answer correct to 2 decimal places.

9.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?

10.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

11.A chord divides a circle into two regions, one larger than the other. Write down the term used for the smaller of these two regions.

12.A bottle holds 2 litres of water. A glass holds 250 ml. Work out how many of these glasses can be filled from one full bottle.

13.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?

14.The diagram shows a solid made from two cuboids joined together. Which shape is the front elevation of this solid?

15.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.