Geometry and measures worksheet — GCSE Foundation

2.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?

3.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

4.How many edges does a triangular prism have?

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

6.A circle has a radius of 3 cm. Work out the diameter of the circle.

7.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.

8.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?

9.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.

10.Write down the exact value of cos 45°.

11.A solid has one curved surface and two flat circular faces of equal size, one at each end. What is the name of this solid?

12.Triangle ABC is similar to triangle PQR. AB corresponds to PQ, and BC corresponds to QR. AB = 5 cm, PQ = 15 cm and BC = 7 cm. Work out the length of QR.

13.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?

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

15.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?