Geometry and measures worksheet — GCSE Foundation

1.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

2.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

3.A diameter divides a circle into two equal halves. Write down the special name given to each of these two halves.

4.Write down the exact value of sin 45°.

5.Priya says: 'To find the arc length of a sector, you divide the circumference by the angle in degrees.' Which statement about Priya's method is correct?

6.How many vertices does a square-based pyramid have?

7.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.

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

9.Point A has coordinates (2, 5). Point A is translated to point B using the column vector with top number 6 and bottom number −3. Write down the coordinates of point B.

10.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.

11.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.

12.In a kite, one pair of opposite angles are equal in size. In kite WXYZ, angle X = 40° and angle Z = 100° are the two angles that are NOT equal to each other. The other two angles, W and Y, are equal to each other. Work out the size of angle W.

13.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?

14.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.

15.A solid has one curved surface and two flat circular faces of equal size, one at each end. What is the name of this solid?