Geometry and measures worksheet — GCSE Foundation

1.In a kite, one pair of opposite angles are equal in size. In kite WXYZ, angle X = 40° and angle Z = 100° are the two angles that are NOT equal to each other. The other two angles, W and Y, are equal to each other. Work out the size of angle W.

2.A vertical line passes through the point (5, 2). Write down the equation of this line.

3.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.

4.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?

5.In a construction, a point P is marked at the foot of the perpendicular drawn from point X to a straight line. Which statement correctly compares the distance XP with the distance from X to any other point on the line?

6.Shape S has a vertex at (9, 6). It is enlarged by a scale factor of 1/3, centre the origin. Work out the coordinates of the image of this vertex.

7.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

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

9.A landscaper marks out two triangular flower beds using stakes and a tape measure. Bed 1 has two edges of 5 m and 7 m, meeting at a corner with a marked angle of 60° between them. Bed 2 has edges of 5 m and 7 m, meeting at a corner also marked at 60° between them. The landscaper wants to check the two beds will be exactly the same size and shape using only these three measurements. Which condition proves the two beds are congruent?

10.Write down the number of lines of symmetry a rhombus has.

11.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.

12.Lines AB and CD cross at a point, forming four right angles where they meet. Which notation correctly describes the relationship between AB and CD?

14.In triangle ABC and triangle DEF, AB = DE, angle ABC = angle DEF and BC = EF. Write down the congruence condition that proves the two triangles are congruent.

15.A parallelogram has a base of 20 cm and a sloping side of 13 cm. The perpendicular drawn from the top of that sloping side down to the base meets the base 5 cm from the foot of the sloping side, so the perpendicular, the 5 cm and the 13 cm sloping side form a right-angled triangle. Work out the area of the parallelogram.