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

Maths · GCSE Foundation · Geometry and measures · Non-calculator · 15 questions

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1.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
2.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.
(a)40 cm²
(b)80 cm²
(c)20 cm²
(d)13 cm²
3.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).
(a)2
(b)−2
(c)8
(d)0.5
4.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.
(a)0
(b)2
(c)4
(d)1
5.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.
(a)(5, 4)
(b)(14, 4)
(c)(8, 2)
(d)(4, 2)
6.A circle is drawn on a page. Write down how many radii can be drawn in the circle.
(a)Infinitely many
(b)Exactly one
(c)Exactly four
(d)Exactly two
7.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
(a)18
(b)36
(c)13
(d)26
8.Two similar triangles have lengths in the ratio 2 : 5. The sides of the smaller triangle are 4 cm, 6 cm and 8 cm. Work out the length of the longest side of the larger triangle.
(a)10 cm
(b)20 cm
(c)3.2 cm
(d)40 cm
9.A straight fence is 5 m long. Describe the shape of the region made up of every point on the ground within 2 m of any part of the fence.
(a)a rounded rectangle: 5 m by 4 m with semicircular ends
(b)a circle of radius 2 m
(c)a rectangle, 9 m by 4 m
(d)a rectangle, 5 m by 2 m
10.Postcard P is similar to postcard Q. The 6 cm side of P corresponds to the 15 cm side of Q, and the 8 cm side of P corresponds to a matching side of Q. Work out the length of that matching side of Q.
(a)3.2 cm
(b)16 cm
(c)17 cm
(d)20 cm
11.The perimeter of a square is 20 cm. Work out the area of the square.
(a)5 cm
(b)25 cm²
(c)100 cm²
(d)400 cm²
12.A rhombus has all four sides equal in length. Which statement about a rhombus is correct?
(a)Its rotational symmetry order is always 4
(b)Its diagonals cross at right angles
(c)Its diagonals are always equal in length
(d)It always has four right angles
13.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.
(a)(1, 7)
(b)(6, 4)
(c)(6, 2)
(d)(−2, 4)
14.A parallelogram has a base of 4 cm and a perpendicular height of 17 cm. Work out the area of the parallelogram.
(a)42 cm
(b)21 cm
(c)34 cm²
(d)68 cm²
15.Triangle ABC has AB = 8 cm, angle B = 50° and BC = 6 cm. Triangle DEF has DE = 8 cm, angle E = 50° and EF = 6 cm. Which condition proves the two triangles are congruent?
(a)AAS - two angles and a non-included side equal
(b)SSS - three sides equal
(c)SAS - two sides and the included angle equal
(d)ASA - two angles and the included side equal

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