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.

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Geometry and measures worksheet — GCSE Foundation

Maths · GCSE Foundation · Geometry and measures · 15 questions

MathsUKwww.geekhero.co.uk

1.A rectangular garden gate is 3 m wide and 4 m high. A straight brace runs from one corner of the gate to the opposite corner. Work out the length of the brace.
(a)7 m
(b)5 m
(c)12 m
(d)25 m
2.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.
(a)(6, 1)
(b)(6, 3)
(c)(2, 3)
(d)(5, 4)
3.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.
(a)1 : 3000
(b)1 : 30
(c)1 : 300
(d)1 : 3
4.Triangle PQR and triangle XYZ have angle P = angle X, angle Q = angle Y and angle R = angle Z, with no side lengths given for either triangle. Which of the following correctly describes the relationship between the two triangles?
(a)Similar, but AAA alone does not prove congruence
(b)Congruent, because AAA proves congruence
(c)No relationship can be determined at all
(d)Congruent, because equal angles force equal sides
5.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.
(a)Angles in a triangle sum to 180°
(b)Angles on a straight line sum to 180°
(c)Vertically opposite angles are equal
(d)Base angles of an isosceles triangle are equal
6.A trapezium has parallel sides of 16 cm and 24 cm, and a perpendicular height of 7 cm. Work out the area of the trapezium.
(a)280 cm²
(b)140 cm²
(c)168 cm²
(d)47 cm
7.A student says the reverse of the translation vector $(- 9 4)$ is $(9 4)$ . Write down the correct reverse translation vector.
(a) $(- 9 - 4)$
(b) $(- 9 4)$
(c) $(9 - 4)$
(d) $(9 4)$
8.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.
(a)48
(b)14
(c)24
(d)28
9.In triangle PQR and triangle STU, PQ = ST, QR = TU and PR = SU. Write down the congruence condition that proves the two triangles are congruent.
(a)SAS
(b)ASA
(c)RHS
(d)SSS
10.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.
(a)(−18, 23)
(b)(22, −13)
(c)(2, 5)
(d)(12, −4)
11.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.
(a)15.7 cm
(b)31.4 cm
(c)62.8 cm
(d)78.5 cm
12.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.
(a)SSS
(b)SAS
(c)RHS
(d)AAS
13.An angle is measured with a protractor as 47°. What type of angle is this?
(a)Reflex
(b)Acute
(c)Obtuse
(d)Right angle
14.Two sides of a triangle are 9 cm and 15 cm long. Write down which one of these lengths is possible for the third side.
(a)24 cm
(b)26 cm
(c)6 cm
(d)10 cm
15.A sector of a circle has angle 120° and an arc length of 31.4 cm. Using π = 3.14, work out the radius of the circle.
(a)5 cm
(b)30 cm
(c)7.5 cm
(d)15 cm

Build your own mix at the worksheet builder.