Geometry and measures worksheet — GCSE Foundation

1.For two triangles to be proved congruent using SAS, which two facts must be true about both triangles?

2.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.

3.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

4.A quadrilateral has exactly two lines of symmetry, its two pairs of opposite angles are equal, and its diagonals are not equal in length. Write down the name of this quadrilateral.

5.Vertex X of a triangle is at (−3, 5). After a translation, the image of X is at (2, −1). Write down the column vector of this translation.

6.m is the column vector with top number 3 and bottom number −4. Which of these column vectors is a scalar multiple of m?

7.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?

8.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.

9.The diagram shows a solid made from two cuboids joined together. Which shape is the front elevation of this solid?

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.A furniture catalogue drawing uses a scale of 1 cm to 1.5 m. A sofa in the drawing is measured as 7 cm long. What is the real length of the sofa, in metres?

12.Write down the mathematical name for a quadrilateral that has exactly one pair of parallel sides.

13.A pop-up canopy has two sloping supports that meet at the top. Each support makes an angle of 30° with the ground and is 6 m long. Using the exact value of cos 30°, work out the total width of the canopy's base.

14.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?

15.A solid has 5 faces, 9 edges and 6 vertices. Two of its faces are triangles and the other three are rectangles. Which solid is it?