Geometry and measures worksheet — GCSE Foundation

1.Two similar triangles have lengths in the ratio 5 : 8. A side of the smaller triangle is 6.5 cm. Work out the length of the corresponding side of the larger triangle.

2.A triangle has vertices A(1, 1), B(5, 1) and C(5, 4). Work out the lengths of AB, BC and CA, and write down whether triangle ABC is right-angled.

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

4.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

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

6.A circle is drawn on a page. Write down how many radii can be drawn in the circle.

7.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?

8.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).

9.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

10.Triangle ABC is right-angled at B. Triangle DEF is right-angled at E. AB = DE = 6 cm and AC = DF = 10 cm (AC and DF are the hypotenuses of their triangles). A student says this is not enough information to prove the triangles are congruent, because only two sides are given. Which reason shows the student is wrong?

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

12.Write down which one of these statements about quadrilaterals is true.

13.A tap fills a tank at a rate of 18 litres per minute. The tank holds 0.45 m³. Work out how long the tap takes to fill the tank.

14.In triangle PQR and triangle STU, PQ = ST, QR = TU and PR = SU. Write down the congruence condition that proves the two triangles are congruent.

15.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.