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 DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.
- 2.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.
- 3.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.
- 4.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?
- 5.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.
- 6.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.
- 7.Two angles lie on a straight line. One angle is 118°. Which reason correctly explains why the other angle is 62°?
- 8.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.
- 9.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.
- 10.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.
- 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.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.
- 13.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.
- 14.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.
- 15.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.
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