Geometry and measures worksheet — GCSE Foundation

1.Write down the column vector, from the options given, that would move a point to the right and downwards.

2.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.

3.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.

4.A chord divides a circle into two regions, one larger than the other. Write down the term used for the smaller of these two regions.

5.A submarine travels due south. What is the three-figure bearing for this direction?

6.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

7.In parallelogram ABCD the vertices are labelled in order round the shape, so angle A and angle B are at the two ends of the same side. Angle A is 70°. Work out the size of angle B.

8.In quadrilateral ABCD, side AB is parallel to side DC. Which statement correctly uses geometric notation to show this?

10.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.

11.Triangle ABC is translated by the column vector with top number 3 and bottom number −5 to form triangle A′B′C′. Triangle A′B′C′ is then translated by the column vector with top number −7 and bottom number 2 to form triangle A″B″C″. Work out the single column vector that translates triangle ABC directly to triangle A″B″C″.

12.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.

13.The diagram shows the plan of the base layer of a solid built from identical cubes. A second layer of cubes is added on top, filling the entire base layer to a height of 2 cubes everywhere. Work out how many squares are visible in the plan view of this solid.

14.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

15.A rectangular photograph is 12 cm long and 5 cm wide. Work out the perimeter of the photograph.