Printable · GCSE Foundation · ages 14-16
Geometry and measures worksheet — GCSE Foundation
Fifteen questions across the geometry and measures statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
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Geometry and measures worksheet — GCSE Foundation
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- 1.Triangle ABC has a right angle at B. Triangle DEF has a right angle at E. The hypotenuse of triangle ABC equals the hypotenuse of triangle DEF, and side AB equals side DE. Which condition proves that the two triangles are congruent?
- 2.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.
- 3.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.
- 4.A point is translated twice by the vector . Write down the single column vector that describes the overall translation.
- 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 DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.
- 7.A drone starts at the point (3.5, −2) on a grid measured in metres. It flies by the vector to check a first sensor. The drone then needs to fly in a straight line to reach the point (−1.7, 9) to check a second sensor. Work out the column vector of this second flight.
- 8.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.
- 9.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.
- 10.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.
- 11.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?
- 12.A robotic arm's tip starts at the point (12.5, −4.25) on a grid measured in centimetres. It moves by the vector to pick up a component, then by the vector to place it. Work out the coordinates of the tip after both moves.
- 13.A rectangular photograph is 12 cm long and 5 cm wide. Work out the perimeter of the photograph.
- 14.Two triangles are proved congruent using the ASA condition. What can be concluded about the two remaining pairs of corresponding sides that were not part of the original ASA facts?
- 15.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.
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