Geometry and measures worksheet — GCSE Foundation

1.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.

2.A solid has 10 vertices and 15 edges. Using the formula F + V − E = 2, work out how many faces it has.

3.A hiker walks due west. What is the three-figure bearing for this direction?

4.Write down how many right angles a rectangle has.

5.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?

6.An isosceles trapezium has exactly one pair of parallel sides, and its two non-parallel sides are equal in length. How many lines of symmetry does it have?

7.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.

8.Triangle A has a vertex at (1, 2). Triangle A is enlarged, centre (1, 1), to give triangle B, whose corresponding vertex is at (1, 5). Work out the scale factor of the enlargement.

9.Triangle ABC has AB = 6 cm, BC = 8 cm and angle B = 90°. Triangle XYZ has XY = 6 cm, YZ = 8 cm and angle Y = 90°. Which congruence statement correctly shows the matching vertices?

10.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).

11.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.

12.Work out the distance between the points (−3, 4) and (5, −2).

14.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

15.A right-angled triangle has two sides of length 5 cm and 12 cm, and the angle between those two sides is 90°. Work out the length of the hypotenuse.