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Geometry — Properties

16 practice questions with full worked solutions. Free, no account needed.

Problems & worked solutions

Problem #0828 UK GCSE

Problem 1 — Angles, Lines & Parallel Lines

Angles on a straight line add up to:

Show answer & worked solution
  1. A. 90∘90^\circ
  2. B. 180∘180^\circ✓ correct
  3. C. 360∘360^\circ
  4. D. 270∘270^\circ

Angles on a straight line add up to 180∘180^\circ.

Problem #0829 UK GCSE

Problem 2 — Angles, Lines & Parallel Lines

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 #0830 UK GCSE

Problem 3 — Angles, Lines & Parallel Lines

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 #0831 UK GCSE

Problem 4 — Angles, Lines & Parallel Lines

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 #0832 UK GCSE

Problem 5 — Congruence

Two shapes are congruent if they are:

Show answer & worked solution
  1. A. the same shape and the same size✓ correct
  2. B. the same shape but any size
  3. C. equal in area only
  4. D. equal in perimeter only

Congruent shapes are exactly the same shape and the same size.

Problem #0833 UK GCSE

Problem 6 — Congruence

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 #0834 UK GCSE

Problem 7 — Congruence

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 8 — Congruence

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.

Problem #0836 UK GCSE

Problem 9 — Triangle & Polygon Angles

The interior angles of a triangle add up to:

Show answer & worked solution
  1. A. 180∘180^\circ✓ correct
  2. B. 360∘360^\circ
  3. C. 90∘90^\circ
  4. D. 540∘540^\circ

The interior angles of a triangle add up to 180∘180^\circ.

Problem #0837 UK GCSE

Problem 10 — Triangle & Polygon Angles

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.

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