Geometry and measures worksheet — GCSE Foundation

1.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.

2.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.

3.A patio plan states: 'Side AB of the patio is parallel to side DC, and AB is longer than DC. Sides BC and AD are not parallel to each other and are not equal in length.' The four sides measure AB = 5.1 m, BC = 3.2 m, DC = 2.8 m and AD = 4.5 m. The tiler needs to order edging strip only for the sides that are not parallel to any other side. What total length of edging strip, in metres, should the tiler order?

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 solid is built from five centimetre cubes, standing side by side on a table in a single straight row. Looking down from directly above (the plan view), how many squares are visible?

6.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.

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

8.Point M lies exactly halfway between point A and point B, with A, M and B all on the same straight line. Which term correctly describes point M?

9.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.

10.A solid pyramid has a square base of side 6 cm. Its apex is directly above the centre of the base, at a vertical height of 8 cm. Work out the volume of the pyramid.

11.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.

12.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.

13.In the RHS congruence condition, which three facts must be true about two triangles for RHS to prove they are congruent?

14.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.

15.Write down the name given to a quadrilateral with exactly one pair of parallel sides.