Printable · GCSE Foundation · ages 14-16

Geometric reasoning and simple proofs worksheet — GCSE Foundation

Fifteen questions on "geometric reasoning and simple proofs" — DfE statement G6. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Geometric reasoning and simple proofs worksheet — GCSE Foundation

Maths · GCSE Foundation · G6 · Geometric reasoning and simple proofs · 15 questions

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1.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.
(a)113°
(b)48°
(c)67°
(d)180°
2.Triangle ABC is extended so that side BC is extended beyond C to a point D, forming exterior angle ACD. Angle BAC = 48° and angle ABC = 67°. Which single angle fact gives angle ACD = 115° in one step, without first working out the interior angle at C?
(a)angles in a triangle add up to 180°
(b)angles on a straight line add up to 180°
(c)exterior angle = sum of the two interior opposite angles
(d)exterior angle is always double the smallest angle
3.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.
(a)142°
(b)40°
(c)38°
(d)398°
4.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.
(a)106°
(b)16°
(c)74°
(d)148°
5.Lines GH and JK are parallel. A straight line crosses GH at point M and crosses JK at point N. Angle HMN = 71°. Angle HMN and angle MNK are alternate angles. Work out angle MNK.
(a)142°
(b)19°
(c)109°
(d)71°
6.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.
(a)228°
(b)48°
(c)66°
(d)132°
7.In triangle ABC, point D lies on side AB and point E lies on side AC, so that DE is parallel to BC. AD = 3 cm, DB = 6 cm and DE = 4 cm. Work out the length of BC.
(a)4 cm
(b)8 cm
(c)10 cm
(d)12 cm
8.Triangle ABC is right-angled at B. Triangle DEF is right-angled at E. AB = DE = 6 cm and AC = DF = 10 cm (AC and DF are the hypotenuses of their triangles). A student says this is not enough information to prove the triangles are congruent, because only two sides are given. Which reason shows the student is wrong?
(a)AAA applies, because both triangles have a right angle
(b)The triangles cannot be proved congruent from this information
(c)RHS applies: the right angle, hypotenuse and one matching side are all equal
(d)SSS applies, because all three sides must be equal in any right-angled triangle
9.Two angles lie on a straight line. One angle is 118°. Which reason correctly explains why the other angle is 62°?
(a)angles round a point add up to 360°
(b)angles on a straight line add up to 180°
(c)vertically opposite angles are equal
(d)angles in a triangle add up to 180°
10.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?
(a)vertically opposite angles are equal
(b)corresponding angles are equal
(c)base angles of an isosceles triangle are equal
(d)angles in a triangle add up to 180°
11.A builder props a straight plank against a vertical wall to reach a window ledge. The foot of the plank is 2.1 m from the base of the wall, and the plank is 3.5 m long. Work out how high up the wall the plank reaches.
(a)4.2 m
(b)2.8 m
(c)1.4 m
(d)7.84 m
12.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.
(a)104°
(b)38°
(c)52°
(d)128°
13.Triangle ABC is similar to triangle PQR. AB corresponds to PQ, and BC corresponds to QR. AB = 5 cm, PQ = 15 cm and BC = 7 cm. Work out the length of QR.
(a)35 cm
(b)7 cm
(c)2.33 cm
(d)21 cm
14.A roof truss is shaped like an isosceles triangle resting on a horizontal ceiling joist. The truss's sloping edges are equal in length, and the angle at its apex is 40°. The ceiling joist continues in a straight line beyond the foot of the truss. Work out the angle between the truss's sloping edge and the extended joist, on the outside of the truss.
(a)110°
(b)70°
(c)140°
(d)20°
15.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.
(a)5.4 m
(b)4 m
(c)9 m
(d)7.2 m

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