Similar triangles

Same shape, proportional sides, equal angles. CAPS Grade 12 definition, worked NSC example and related euclidean geometry practice.

Same shape, proportional sides, equal angles.

Definition

Two triangles are similar when their corresponding angles are equal, which makes their corresponding sides proportional. Similarity is the basis of most proportionality proofs in CAPS Euclidean geometry.

Worked example

If △ABC ||| △DEF then AB/DE = BC/EF = AC/DF.

If △ABC ||| △DEF with AB = 6, DE = 9 and BC = 8, then EF/BC = DE/AB = 9/6, so EF = 12.

Where it appears in the exam

Paper 2 asks you to prove two triangles similar and then use their proportional sides to find a length or prove a ratio.

Step-by-step method

  1. Name the triangles with corresponding vertices in the same order.
  2. Prove two pairs of angles equal, with reasons.
  3. Conclude that the triangles are similar (∠∠∠).
  4. Write the proportional sides and solve.

Common mistake

Listing the vertices in the wrong order, so the wrong sides are matched.

Related euclidean geometry terms

Frequently asked questions

What does similar triangles mean in Grade 12 Maths?

Two triangles are similar when their corresponding angles are equal, which makes their corresponding sides proportional. Similarity is the basis of most proportionality proofs in CAPS Euclidean geometry.

Which NSC paper tests similar triangles?

Similar triangles belongs to the Euclidean geometry section of CAPS Grade 12 Mathematics, which is examined in Paper 2.

How do I practise questions involving similar triangles?

Snap a question that uses similar triangles into the Snap&Learn AI solver, or work through the euclidean geometry topic guide and NSC past papers.

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