Geometry and measures worksheet — GCSE Foundation

1.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?

2.A tangent to a circle touches the circle at exactly one point, P. Work out the size of the angle between the tangent and the radius drawn to P.

3.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.

4.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

5.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?

6.A regular nonagon has 9 sides. Work out the sum of its interior angles.

7.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.

8.Which of the following is NOT one of the four basic conditions used to prove two triangles are congruent?

9.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.

10.Triangle ABC is translated by the column vector with top number 3 and bottom number −5 to form triangle A′B′C′. Triangle A′B′C′ is then translated by the column vector with top number −7 and bottom number 2 to form triangle A″B″C″. Work out the single column vector that translates triangle ABC directly to triangle A″B″C″.

11.Which of these correctly compares a 'line' with a 'line segment'?

12.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

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

14.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

15.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.