Geometry and measures worksheet — GCSE Foundation

1.Two triangular offcuts of wood, PQR and STU, are cut for a construction project. PQ = 8 cm, QR = 6 cm and angle PQR = 90°. ST = 8 cm, TU = 6 cm and angle STU = 90°. A carpenter wants to check the two pieces are identical in shape and size before using them as a matching pair. Using only the measurements given, and without working out any further lengths, which condition proves that triangle PQR is congruent to triangle STU?

2.Each of these has an exact value. Write down the one whose value is the greatest.

3.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

4.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

5.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.

6.A quadrilateral has exactly two lines of symmetry, its two pairs of opposite angles are equal, and its diagonals are not equal in length. Write down the name of this quadrilateral.

7.A straight line crosses two parallel lines. An angle of 65° is formed at one crossing. At the other crossing, the angle that lies between the two parallel lines on the opposite side of the crossing line is also 65°. Write down the angle fact that explains why these two angles are equal.

8.Which of the following correctly describes what it means for two lines to be perpendicular?

9.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.

10.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.

11.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?

12.A stained-glass window panel is designed as a kite. Two adjacent sides are each 25 cm, and the other two adjacent sides are each 40 cm. A frame is fitted around the whole panel. The frame costs £2.50 per metre, sold only in whole metres. Work out the total cost of the frame.

13.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.

14.A triangular badge has two sides of length 8 cm and a third side of length 5 cm. Work out the perimeter of the badge.

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