Geometry and measures worksheet — GCSE Foundation

1.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.

2.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.

3.Triangles LMN and XYZ have LM = XY, MN = YZ and LN = XZ. Give a reason why triangle LMN is congruent to triangle XYZ.

4.A ramp's sloped surface crosses two horizontal parallel rails. At the top rail, the angle between the ramp and the rail on the right of the ramp is (3x + 10)°. At the bottom rail, the angle between the ramp and the rail on the left of the ramp is (5x − 30)°. Work out the value of x.

5.In kite WXYZ, WX = WZ and XY = ZY (so at each of X and Z, one side from each of the two unequal pairs meets). Angle X = 100°. Work out angle Z.

6.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?

7.In quadrilateral ABCD the two sides AB and BC are each 6 cm long and meet each other at B. The two sides CD and DA are each 9 cm long and meet each other at D. No side of ABCD is parallel to any other side. Write down the mathematical name of this quadrilateral.

8.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

9.The cross-section of a tent is an isosceles triangle. The angle at the top, between the two equal sloping sides, is 62°. The other two angles are equal to each other. Work out the size of each of those two angles.

10.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?

11.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.

12.A straight line crosses a pair of parallel lines. At one of the crossing points, one of the four angles measures 55°. Work out the size of the angle next to it on a straight line at that crossing point.

13.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.

14.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

15.A rectangular photograph is 12 cm long and 5 cm wide. Work out the perimeter of the photograph.