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Geometry — Properties practice questions — Honors Math

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

Problems & worked solutions

Problem #0841 UK GCSE

Problem 1 — Geometry — Properties

A photo 44 cm by 66 cm is enlarged by scale factor 33. Its new size is:

Show answer & worked solution
  1. A. 1212 cm by 1818 cm✓ correct
  2. B. 77 cm by 99 cm
  3. C. 44 cm by 1818 cm
  4. D. 1212 cm by 66 cm

4×3=124 \times 3 = 12 and 6×3=186 \times 3 = 18, so 1212 cm by 1818 cm.

Problem #0830 UK GCSE

Problem 2 — 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 #0833 UK GCSE

Problem 3 — 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 #0836 UK GCSE

Problem 4 — Geometry — Properties

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 #0840 UK GCSE

Problem 5 — 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 #0837 UK GCSE

Problem 6 — 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 #0829 UK GCSE

Problem 7 — 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 8 — 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 #0842 UK GCSE

Problem 9 — 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 #0843 UK GCSE

Problem 10 — Geometry — Properties

A rectangle 22 cm by 33 cm is similar to a larger rectangle whose shorter side is 88 cm. Its longer side is:

Show answer & worked solution
  1. A. 1212 cm✓ correct
  2. B. 99 cm
  3. C. 2424 cm
  4. D. 66 cm

Scale factor =8÷2=4= 8 \div 2 = 4; longer side =3×4=12= 3 \times 4 = 12 cm.

6 more Geometry — Properties questions in the app

Also covered in Geometry — Properties practice across every exam.

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