Geometry and measures worksheet — GCSE Foundation

1.Which of these describes an obtuse angle?

2.A quadrilateral has vertices A(1, 1), B(5, 1), C(6, 4) and D(2, 4). By comparing the y-coordinates of A, B and of D, C, write down whether the sides AB and DC are parallel, and give a reason for your answer.

4.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?

5.A circle has centre O. PQ, RS and TU are three chords of the circle, and only one of them passes through O. Write down what this tells you about that chord.

6.Triangle ABC has AB = 10 cm, BC = 7 cm and angle A = 40°. Triangle DEF has DE = 10 cm, EF = 7 cm and angle D = 40°. Sam says the two triangles are congruent by SAS. Which statement about Sam's claim is correct?

7.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.

8.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.

9.Triangle ABC has angle A = 40°, angle B = 65° and AB = 10 cm. Triangle DEF has angle D = 40°, angle E = 65° and DE = 10 cm. Which condition proves the two triangles are congruent?

10.A circle has a radius of 3 cm. Work out the diameter of the circle.

11.Write down the exact value of tan 60°.

12.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?

13.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

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 triangle has vertices X, Y and Z, with a right angle at Y. Side XY is twice as long as side YZ. Which of the following correctly describes this triangle?