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 · Non-calculator · 15 questions

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1.Triangle PQR has angle P = 90°. The side PQ = 9 cm and the hypotenuse QR = 15 cm. Work out the length of PR.
(a)17.5 cm
(b)24 cm
(c)12 cm
(d)6 cm
2.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.
(a)75°
(b)105°
(c)37°
(d)146°
3.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.
(a)260°
(b)280°
(c)70°
(d)80°
4.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
5.Lines JK and LM are parallel. A straight line crosses JK at point P and crosses LM at point Q. Angle KPQ = 118°. Angle KPQ and angle MQP are co-interior (allied) angles. Work out angle MQP.
(a)62°
(b)59°
(c)90°
(d)118°
6.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
7.A children's slide is built as a right-angled triangle: the vertical ladder side is 2.4 m, the horizontal base along the ground is 3.2 m, and the sloping slide is the third side. Work out the exact length of the sloping slide.
(a)5.6 m
(b)16 m
(c)3.87 m
(d)4 m
8.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°
9.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.
(a)56°
(b)146°
(c)34°
(d)124°
10.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
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.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.
(a)64°
(b)32°
(c)58°
(d)122°
13.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.
(a)143°
(b)153°
(c)37°
(d)53°
14.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°
15.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?
(a)opposite angles of a parallelogram are equal
(b)co-interior angles add up to 180°
(c)alternate angles are equal
(d)angles on a straight line add up to 180°

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