Geometry and measures worksheet — GCSE Foundation

1.Triangles ABE and CDE share the vertex E, where lines AC and BD cross at E. AE equals CE, and BE equals DE. Angle AEB and angle CED are formed as vertically opposite angles where the lines cross. Which condition proves that triangle ABE is congruent to triangle CDE?

2.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.

3.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?

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

5.In this question, a curved surface counts as a face. How many faces does a cone have?

6.A garden bed is designed as a trapezium. The two parallel sides are 8 m and 12 m, and the perpendicular distance between them is 5 m. Grass seed covers 4 m² per bag, sold only in whole bags. Work out how many bags of grass seed are needed.

7.The bearing of a campsite B from a walker's position A is 070°. What is the bearing of A from B?

8.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.

10.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.

11.Triangle ABC has AB = 5 cm, BC = 7 cm and CA = 9 cm. Triangle DEF has DE = 5 cm, EF = 7 cm and FD = 9 cm. Which condition proves the two triangles are congruent?

12.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

13.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

14.In triangle ABC the base BC is 10 cm long and the sloping side AB is 13 cm long. The perpendicular height from A down to BC is 12 cm. Work out the area of triangle ABC.

15.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.