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Prove / Show That

Afrikaans: Bewys / Toon dat

Demonstrate, using logical algebraic or geometric steps, that a given statement is true. You may not assume the result and work backward from it, if the conclusion appears anywhere as an unproven step in your working, the proof is circular and earns no marks. You must start from what is given or known, and arrive at the stated result as your final line.

Common mistake

The most common error is working from both sides simultaneously, writing LHS = RHS and manipulating both sides toward a common middle expression. This is circular reasoning: it assumes the equality you are trying to prove. You must start from ONE side only (usually the more complex side) and work until it exactly matches the other side, without touching the other side at all. In Euclidean Geometry, every step must also include a stated reason, stating a conclusion without the matching theorem earns no marks.

Signal phrases

These are the words that tell you this instruction is being used.

  • Prove that...
  • Show that the value of... equals...
  • Show that AB is a tangent to the circle
  • Prove that the roots of the equation are real
  • Show that the triangles are similar

Past paper examples

Prove that AB is a tangent to the circle at point B.

Source: DBE Mathematics Paper 2, November 2023, Question 8.3

Show that the roots of the equation are real for all values of k.

Source: DBE Mathematics Paper 1, November 2022, Question 3.4

Test yourself

Before you read the answer, what is this question asking you to do?

Prove that: (x² − y²) / (x + y) = x − y, where x ≠ −y.

Practice question: not from a past paper

Where this comes up