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Geometry — Properties practice questions — GCSE Maths

16 free multiple-choice problems on geometry — properties, ordered to match GCSE Maths difficulty, each with a full worked solution. No account needed — and there's a fresh problem set every day.

Problems & worked solutions

Problem #0833 UK GCSE

Problem 1 — Geometry — Properties

Which transformation always gives an image congruent to the original?

Show answer & worked solution
  1. A. enlargement with scale factor 22
  2. B. reflection✓ correct
  3. C. enlargement with scale factor 12\tfrac{1}{2}
  4. D. a one-way stretch

A reflection keeps size and shape unchanged, so the image is congruent. Enlargements with scale factor ≠1\neq 1 change the size.

Problem #0831 UK GCSE

Problem 2 — Geometry — Properties

When two straight lines cross, vertically opposite angles are:

Show answer & worked solution
  1. A. equal✓ correct
  2. B. adding to 180∘180^\circ
  3. C. adding to 90∘90^\circ
  4. D. adding to 360∘360^\circ

Vertically opposite angles are equal.

Problem #0837 UK GCSE

Problem 3 — Geometry — Properties

The interior angles of a quadrilateral add up to:

Show answer & worked solution
  1. A. 360∘360^\circ✓ correct
  2. B. 180∘180^\circ
  3. C. 540∘540^\circ
  4. D. 720∘720^\circ

2×180∘=360∘2 \times 180^\circ = 360^\circ.

Problem #0840 UK GCSE

Problem 4 — Geometry — Properties

Two shapes are similar if they have:

Show answer & worked solution
  1. A. the same shape, with lengths in the same ratio✓ correct
  2. B. the same size
  3. C. equal areas
  4. D. no fixed relationship

Similar shapes are the same shape with all lengths in the same ratio (a scale factor).

Problem #0829 UK GCSE

Problem 5 — Geometry — Properties

Angles around a point add up to:

Show answer & worked solution
  1. A. 180∘180^\circ
  2. B. 360∘360^\circ✓ correct
  3. C. 90∘90^\circ
  4. D. 720∘720^\circ

Angles around a point add up to 360∘360^\circ.

Problem #0838 UK GCSE

Problem 6 — Geometry — Properties

Each interior angle of an equilateral triangle is:

Show answer & worked solution
  1. A. 60∘60^\circ✓ correct
  2. B. 90∘90^\circ
  3. C. 180∘180^\circ
  4. D. 45∘45^\circ

180∘÷3=60∘180^\circ \div 3 = 60^\circ.

Problem #0830 UK GCSE

Problem 7 — Geometry — Properties

Two angles lie on a straight line. One is 110∘110^\circ. The other is:

Show answer & worked solution
  1. A. 70∘70^\circ✓ correct
  2. B. 250∘250^\circ
  3. C. 90∘90^\circ
  4. D. 110∘110^\circ

180∘−110∘=70∘180^\circ - 110^\circ = 70^\circ.

Problem #0842 UK GCSE

Problem 8 — Geometry — Properties

Two similar triangles have bases 55 cm and 1515 cm. The scale factor (small to large) is:

Show answer & worked solution
  1. A. 33✓ correct
  2. B. 13\tfrac{1}{3}
  3. C. 1010
  4. D. 7575

15÷5=315 \div 5 = 3.

Problem #0834 UK GCSE

Problem 9 — Geometry — Properties

A triangle has sides 3,4,53, 4, 5 cm. A triangle congruent to it has sides:

Show answer & worked solution
  1. A. 3,4,53, 4, 5 cm✓ correct
  2. B. 6,8,106, 8, 10 cm
  3. C. 1.5,2,2.51.5, 2, 2.5 cm
  4. D. 3,4,63, 4, 6 cm

Congruent triangles have equal corresponding sides, so 3,4,53, 4, 5 cm.

Problem #0835 UK GCSE

Problem 10 — Geometry — Properties

Are two squares that each have side 55 cm congruent?

Show answer & worked solution
  1. A. Yes✓ correct
  2. B. No
  3. C. Only if one is rotated
  4. D. It cannot be decided

Both are squares of side 55 cm — same shape and size — so they are congruent.

6 more Geometry — Properties questions in the app

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