Geometry and measures worksheet — GCSE Foundation

1.A hiker walks due west. What is the three-figure bearing for this direction?

2.A triangle has vertices X, Y and Z, with a right angle at Y. Side XY is twice as long as side YZ. Which of the following correctly describes this triangle?

3.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

4.A polygon has 9 sides. What is the name of this polygon?

5.Triangle ABC has AB = 8 cm, angle B = 50° and BC = 6 cm. Triangle DEF has DE = 8 cm, angle E = 50° and EF = 6 cm. Which condition proves the two triangles are congruent?

6.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.

7.A sector of a circle has angle 120° and an arc length of 31.4 cm. Using π = 3.14, work out the radius of the circle.

8.A radar station is at the origin of a grid, where each unit represents 1 km. A boat is detected at the point (7, 24). Work out the boat's distance from the station, then work out how many hours it will take the boat to reach the station travelling directly towards it at 5 km per hour.

9.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.

10.Work out the exact value of sin 45° × cos 45°.

11.p is the column vector with top number 4 and bottom number −3. Work out 2p, giving your answer as a column vector in the form (top, bottom).

12.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.

13.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

14.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.

15.A quadrilateral has both pairs of opposite sides parallel and equal in length, but none of its angles are right angles. Which statement about this quadrilateral is correct?