Geometry and measures worksheet — GCSE Foundation

1.A running track has a straight section and a semicircular bend. The bend is a semicircle with radius 32 m. Work out the length of the curved part of the bend, to 1 decimal place. (Use π = 3.14.)

2.A map has a scale of 1 cm : 5 km. A road is drawn 3 cm long on the map. What is the real length of the road?

3.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.

4.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

5.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.

6.Which pair of points lies on a horizontal line when the points are plotted on a coordinate grid?

7.The three angles of a triangle are 10°, 58° and 112°. Write down the name that describes this triangle.

8.A perpendicular bisector is drawn through the midpoint of a line segment AB. Which set of points does this construction show?

9.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?

10.A scale drawing of a rectangular lawn uses a scale of 1 : 125. On the drawing, the lawn measures 4 cm by 2.4 cm. Work out the perimeter of the real lawn, in metres.

11.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?

12.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.

13.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.

14.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?

15.Triangle ABC is similar to triangle PQR. AB corresponds to PQ, and BC corresponds to QR. AB = 5 cm, PQ = 15 cm and BC = 7 cm. Work out the length of QR.