Geometry and measures worksheet — GCSE Foundation

1.A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.

2.A triangle has vertices A(1, 1), B(5, 1) and C(5, 4). Work out the lengths of AB, BC and CA, and write down whether triangle ABC is right-angled.

3.In this question, a curved surface counts as a face. How many faces does a sphere have?

4.Write down the name given to a quadrilateral that has exactly one pair of parallel sides.

5.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.

6.A trapezium has parallel sides of 16 cm and 24 cm, and a perpendicular height of 7 cm. Work out the area of the trapezium.

7.A rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.

8.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.

9.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.

10.m is the column vector with top number 3 and bottom number −4. Which of these column vectors is a scalar multiple of m?

11.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?

12.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

13.Write down the exact value of sin 45°.

14.In triangle ABC and triangle DEF, the angle at A and the angle at D are both 40°, and the angle at B and the angle at E are both 70°. No side lengths are given. Write down whether the two triangles must be similar, with the reason.

15.A written description of a diagram states: 'AB is marked with a single arrow, CD is marked with a single arrow, and EF is marked with a double arrow.' Using the standard convention for marking parallel lines, what can be concluded?