Geometry and measures worksheet — GCSE Foundation

1.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

2.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?

3.Write down the exact value of cos 45°.

4.Three of these are rational numbers and one is irrational. Write down the one that is irrational.

5.A square-based pyramid is cut by a flat plane parallel to its base, partway up between the base and the apex. What shape is the cross-section?

6.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?

7.A jug holds 750 ml of water. Work out what fraction of a litre this is.

8.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.

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.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.

11.A cube has all of its edges the same length. How many planes of symmetry does it have?

13.Which of these correctly compares a 'line' with a 'line segment'?

14.A path goes from A(1, 1) to B(1, 5), then from B to C(6, 5). Work out the total length of the path from A to C.

15.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.