Geometry and measures worksheet — GCSE Foundation

1.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.

2.Which of the following is NOT one of the four basic conditions used to prove two triangles are congruent?

3.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.

4.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.

5.A sector of a circle has an angle of 150°. Work out what fraction of the circle's area the sector is.

6.A designer creates a repeating tile pattern. Each tile is translated from the one before it by the column vector with top number 4.5 and bottom number −2.5 (in centimetres). The first tile has its bottom-left corner at (1.5, 3). Work out the coordinates of the bottom-left corner of the third tile.

7.Two triangles are congruent to each other. What does this tell you about their angles and sides?

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

9.Which of the following is the correct definition of a regular polygon?

10.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?

11.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.

12.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.

13.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.

14.A regular nonagon has 9 sides. Work out the sum of its interior angles.

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