C
CraftExam
medium difficulty5 min

AAA similarity criterion

If three angles of one triangle are respectively equal to three angles of another triangle, the triangles are similar.

In one line: Three equal angles, one same shape.

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Understand it

The third angle automatically matches because the angle sum of a triangle is 180°. So once two corresponding angles are equal, the full shape pattern is fixed.

Example

If one triangle has angles 35°, 75°, 70° and another triangle has the same angle pattern, the triangles are similar by AAA.

Formula and rule

AAA similarity: three corresponding angles equal implies similarity.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

  1. 1In triangles ABC and DEF, if ∠A = ∠D = 40° and ∠B = ∠E = 65°, then ∠C = ∠F = 75°.
  2. 2The triangles are similar by AAA.

Method you can reuse

  1. 1Check the first two corresponding angles.
  2. 2Confirm the third angle using angle sum if needed.
  3. 3State AAA similarity clearly.

Sketch it in your answer

Mark the equal angles on the corresponding corners and keep the vertex order the same.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What does AAA similarity tell you when all corresponding angles of two triangles match?

Think first, then show answer
AAA similarity tells us that the triangles are similar because equal angles fix the shape completely. Their sides may be different in size, but the triangle pattern remains the same.

Common wrong answer

Thinking side lengths must also be given. For AAA, matching angles are already sufficient.

Don't mix this up

Students sometimes wait for side lengths even after all the corresponding angles have already matched.

Exam tip

If two corresponding angles match, the third one will also match because the total is always 180°.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

A proof or short-answer question may give angles and ask for the correct similarity reason.
  1. 1

    Enough for 1 mark

    If three angles of one triangle are respectively equal to three angles of another triangle, the triangles are similar.

  2. 2

    Add for 2 marks

    Example: If one triangle has angles 35°, 75°, 70° and another triangle has the same angle pattern, the triangles are similar by AAA.

  3. 3

    Add for 3 marks

    The third angle automatically matches because the angle sum of a triangle is 180°.

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