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.
Geometric reasoning and simple proofs worksheet — GCSE Foundation
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- 1.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.
- 2.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.
- 3.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?
- 4.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.
- 5.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.
- 6.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?
- 7.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.
- 8.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.
- 9.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.
- 10.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.
- 11.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.
- 12.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.
- 13.Triangles LMN and XYZ have LM = XY, MN = YZ and LN = XZ. Give a reason why triangle LMN is congruent to triangle XYZ.
- 14.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.
- 15.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.
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