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.

Non-calculator

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

Geometric reasoning and simple proofs worksheet — GCSE Foundation

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

MathsUKwww.geekhero.co.uk

1.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
2.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°
3.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
4.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
5.Lines PQ and RS are parallel. A straight line crosses PQ at point X and crosses RS at point Y. Angle PXY = 63°. Angle PXY and angle XYS are co-interior (allied) angles, which add up to 180°. Work out the size of angle XYS.
(a)27°
(b)90°
(c)117°
(d)63°
6.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
7.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°
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 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°
10.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
11.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°
12.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°
13.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
14.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.
(a)56°
(b)146°
(c)34°
(d)124°
15.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.
(a)64°
(b)32°
(c)58°
(d)122°

Build your own mix at the worksheet builder.