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Mathematics P2 Step 6 of 9 beginner

Similarity, Proportion and Geometry Proofs

Prove triangles similar, use the proportion theorem correctly, and set up ratios that give the right answer every time.

By the end, you can

prove two triangles similar, apply the proportion theorem and use similarity to find unknown lengths.

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Similarity, Proportion and Geometry Proofs

QUEST MATH-P2-SIMILARITY

Same shape, different size

Two triangles are similar when they have the same shape: equal angles, and sides in the same proportion. They are congruent when they are also the same size. 🔺

Similar triangles are how you find a length you cannot measure — the height of a building from its shadow, a distance across a river. In Paper 2 they are how most "find the length of DE" questions are solved.

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What you'll cover

  1. 1 Same shape, different sizefree preview above
  2. 2 Similar or congruent
  3. 3 Naming triangles in the right order
  4. 4 Setting up the ratio
  5. 5 The proportion theorem
  6. 6 Areas, and a proof that gets asked
  7. 7 A routine for similarity questions
  8. 8 The challenge
  9. 9 What to take with you

Your certificate

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Similarity, Proportion and Geometry Proofs

LCA-2026-••••••••

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Informal learning, not an accredited qualification.

Next on the Mathematics P2 path · step 7 of 9

Sine Rule, Area Rule and Applied Trigonometry

14 min · R19

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Similarity, Proportion and Geometry Proofs: questions

How long does Similarity, Proportion and Geometry Proofs take?
About 14 minutes: 9 short lessons, 2 quick checks and a 5-question final challenge. Your progress is saved after every step, so you can stop and carry on later.
How much does Similarity, Proportion and Geometry Proofs cost?
R19, paid securely online, or 19 learning credits from your wallet. You pay once: if you don’t pass the challenge, you try again at no extra cost.
What do I need to pass?
4 out of 5 on the final challenge (80%). The quick checks along the way help you learn and do not count towards your mark.
Is the certificate accredited?
No. A MicroQuest is informal learning. Your certificate proves you completed it and has a number and QR code anyone can verify, but it is not an accredited qualification or SETA/QCTO credits, and it says so.
Can I do it on my phone?
Yes. Tap Start to learn in your phone’s browser, or send QUEST MATH-P2-SIMILARITY to 076 263 6000 on WhatsApp. It is the same MicroQuest and the same certificate either way.

Similarity, Proportion and Geometry Proofs

R19 · 14 min · certificate

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