Geometry and measures worksheet — GCSE Foundation

1.In an isosceles triangle each of the two base angles is 46°. Work out the size of the angle at the apex.

2.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.

3.p is the column vector with top number 5 and bottom number 1. q is the column vector with top number −2 and bottom number 3. Work out p − 2q, giving your answer as a column vector in the form (top, bottom).

4.A line segment joins two points on the circumference of a circle, without necessarily passing through the centre. Write down the general term for this line segment.

5.A stained-glass window panel is designed as a kite. Two adjacent sides are each 25 cm, and the other two adjacent sides are each 40 cm. A frame is fitted around the whole panel. The frame costs £2.50 per metre, sold only in whole metres. Work out the total cost of the frame.

6.A sign-maker is told a metal bracket outline must have two pairs of adjacent sides equal in length (not opposite pairs), exactly one pair of opposite angles equal, and exactly one line of symmetry. Which quadrilateral matches this description?

7.Point B is at (1, 6). It is reflected in the x-axis. Work out the coordinates of the image of point B.

8.An angle is measured with a protractor as 47°. What type of angle is this?

9.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

10.A builder lays a low wall made from identical bricks. The diagram shows the plan of the wall's footprint on a grid, where each square is one brick. The wall is built up to a height of 4 bricks everywhere. Work out the total number of bricks used.

11.A circle has a radius of 1 cm. Work out the circumference of the circle. Give your answer in terms of π.

12.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?

13.A rectangular name card has a perimeter of 30 cm. The card is 9 cm long. Work out the width of the card.

14.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?

15.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?