Geometry and measures worksheet — GCSE Foundation

1.Write down the term for the distance all the way around the edge of a circle.

2.Postcard P is similar to postcard Q. The 6 cm side of P corresponds to the 15 cm side of Q, and the 8 cm side of P corresponds to a matching side of Q. Work out the length of that matching side of Q.

3.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?

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

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

6.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.

7.A designer enlarges a drawing of a model car for a poster. She first enlarges the drawing by a scale factor of 1.5, and then enlarges that result by a further scale factor of 2. On the original drawing, the position of a wheel relative to the front bumper is given by the column vector with top number 4 and bottom number −3, in centimetres. What is the corresponding column vector on the poster, in centimetres?

8.The diagram shows a prism resting on a table. Which shape is its front elevation, the view looking at it from directly in front?

9.A quadrilateral has all four sides equal in length and all four interior angles equal to 90°. Its diagonals are equal in length and bisect each other at right angles. Which quadrilateral matches this description exactly?

10.Two triangles are proved congruent using the ASA condition. What can be concluded about the two remaining pairs of corresponding sides that were not part of the original ASA facts?

11.Triangles PQS and RQS share the common side QS. PQ equals RQ, and PS equals RS. Which condition proves that triangle PQS is congruent to triangle RQS?

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

13.A trapezium has parallel sides of 16 cm and 24 cm, and a perpendicular height of 7 cm. Work out the area of the trapezium.

14.A polygon has 9 sides. What is the name of this polygon?

15.A solid has 6 faces: one pentagon and five triangles that all meet at a single point above the pentagon. What is the name of this solid?