Geometry and measures worksheet — GCSE Foundation

1.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?

2.Triangle ABC has AB = 5 cm, BC = 7 cm and CA = 9 cm. Triangle DEF has DE = 5 cm, EF = 7 cm and FD = 9 cm. Which condition proves the two triangles are congruent?

3.A scale model of a bridge is built so that 2 cm on the model represents 5 m of the real bridge. The real bridge is 45 m long. Work out the length of the model bridge, in centimetres.

4.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.

5.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

6.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.

7.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.

8.Quadrilateral WXYZ has WX parallel to ZY, and WZ = XY (the two non-parallel sides are equal in length). Give a reason why angle W = angle X.

9.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.

10.Work out the exact value of sin 30° + cos 60°.

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

12.e is the column vector with top number 5 and bottom number k. f is the column vector with top number 15 and bottom number 6. Given that f is 3 times e, work out the value of k.

13.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).

14.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.

15.Freya is designing a triangular flower bed. Two of its corners have equal angles, and the angle at the third corner is 40°. Work out the size of one of the two equal corner angles.