Geometry and measures worksheet — GCSE Foundation

1.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.

2.The diagram shows a solid resting on its side on a table. Work out which shape is its plan view, the view looking straight down from above.

3.Triangle A has a vertex at (1, 2). Triangle A is enlarged, centre (1, 1), to give triangle B, whose corresponding vertex is at (1, 5). Work out the scale factor of the enlargement.

4.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.

5.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

6.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

7.A builder props a straight plank against a vertical wall to reach a window ledge. The foot of the plank is 2.1 m from the base of the wall, and the plank is 3.5 m long. Work out how high up the wall the plank reaches.

8.The perimeter of a square is 20 cm. Work out the area of the square.

9.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?

10.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.

11.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?

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

13.A scale drawing of a bridge uses a scale of 1 : 25. A support beam on the drawing measures 4.4 cm. What is the real length of the beam, in metres?

14.The diagram shows a prism resting on a table. Which shape is its front elevation, the view looking at it from directly in front?

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?