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
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- 1.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.
- 2.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.
- 3.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.
- 4.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.
- 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.
- 6.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.
- 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.
- 8.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.
- 9.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.
- 10.A rectangular gate is braced with a diagonal strut. The gate is 1.2 m wide and 0.9 m tall. Work out the exact length of the diagonal strut.
- 11.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.
- 12.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?
- 13.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?
- 14.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.
- 15.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.
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