Geometry and measures worksheet — GCSE Foundation

1.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.

2.A polygon has 12 straight sides. What is the mathematical name for this polygon?

3.Work out the distance between the points (−3, 4) and (5, −2).

4.A solid is built from centimetre cubes standing on a table. Seen from the front, the left-hand column is 2 cubes high, the middle column is 2 cubes high and the right-hand column is 1 cube high. Work out how many squares make up the front elevation.

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

6.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.

7.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.

8.Triangle ABC is right-angled at B. Triangle DEF is right-angled at E. AB = DE = 6 cm and AC = DF = 10 cm (AC and DF are the hypotenuses of their triangles). A student says this is not enough information to prove the triangles are congruent, because only two sides are given. Which reason shows the student is wrong?

9.A circle is drawn on a page. Write down how many radii can be drawn in the circle.

10.A garden bed is designed as a trapezium. The two parallel sides are 8 m and 12 m, and the perpendicular distance between them is 5 m. Grass seed covers 4 m² per bag, sold only in whole bags. Work out how many bags of grass seed are needed.

11.A straight line crosses a pair of parallel lines. At one of the crossing points, one of the four angles measures 55°. Work out the size of the angle next to it on a straight line at that crossing point.

12.The three angles of a triangle are 10°, 58° and 112°. Write down the name that describes this triangle.

13.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?

14.How many vertices does a cylinder have?

15.Triangle ABC has AB = 10 cm, BC = 7 cm and angle A = 40°. Triangle DEF has DE = 10 cm, EF = 7 cm and angle D = 40°. Sam says the two triangles are congruent by SAS. Which statement about Sam's claim is correct?