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.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.
- 2.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.
- 3.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.
- 4.Triangle PQR has angle P = 90°. The side PQ = 9 cm and the hypotenuse QR = 15 cm. Work out the length of PR.
- 5.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.
- 6.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.
- 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.
- 8.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.
- 9.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.
- 10.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.
- 11.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.
- 12.Two angles lie on a straight line. One angle is 118°. Which reason correctly explains why the other angle is 62°?
- 13.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?
- 14.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.
- 15.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.
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