Geometry and measures worksheet — GCSE Foundation

1.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?

2.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.

3.Two straight paths cross at a junction in a park. One of the angles between them, measured with a protractor, is 76°. What is the size of the angle immediately next to it on a straight line?

4.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

5.A solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.

6.Work out the exact value of (sin 30°)² + (cos 30°)².

7.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

8.Line 1 passes through (0, 1) and (2, 5). Line 2 passes through (3, 2) and (5, 6). Work out the gradient of each line. Then write down whether the two lines are parallel.

9.How many edges does a triangular prism have?

10.A landscaper marks out two triangular flower beds using stakes and a tape measure. Bed 1 has two edges of 5 m and 7 m, meeting at a corner with a marked angle of 60° between them. Bed 2 has edges of 5 m and 7 m, meeting at a corner also marked at 60° between them. The landscaper wants to check the two beds will be exactly the same size and shape using only these three measurements. Which condition proves the two beds are congruent?

11.Work out the distance between the point (0, 0) and the point (5, 12).

12.Write down the name given to a quadrilateral that has exactly one pair of parallel sides.

13.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.

14.ABCD is an isosceles trapezium. The sides AB and DC are parallel, and the two sloping sides AD and BC are equal in length. Angle D is 112°. Work out the size of angle B.

15.Point C is at (2, 3). It is rotated 90° clockwise about the origin. Work out the coordinates of the image of point C.