Geometry and measures worksheet — GCSE Foundation

1.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

2.A circle has centre O. Radii OA and OB are drawn, together with the arc AB, enclosing a sector. The straight chord AB is also drawn. Write down the name of the region enclosed between the chord AB and the arc AB.

3.Work out the exact value of (sin 30°)² + (cos 30°)².

4.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?

5.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.

6.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.

7.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.

8.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.

9.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.

10.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

11.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.

12.A conservatory has a roof panel shaped like a regular octagon. Work out the interior angle of the octagon, then use it to work out the size of the reflex angle at the same vertex, on the outside of the roof panel.

13.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.

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

15.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.