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medium difficulty5 min

Similarity of triangles

Two triangles are similar when their corresponding angles are equal and their corresponding sides are in the same ratio.

In one line: Same shape, different size.

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Understand it

Similarity means the triangles have the same shape, even if one is larger or smaller. The angle pattern stays the same, and every matching side changes by a fixed scale factor.

Example

Triangles with sides 3 cm, 4 cm, 5 cm and 6 cm, 8 cm, 10 cm are similar because each matching side is in the ratio 1:2.

Formula and rule

Corresponding angles are equal, and corresponding sides are proportional in similar triangles.

See it worked out

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

Worked example

  1. 1For triangles with sides 3, 4, 5 and 6, 8, 10, each side in the second triangle is twice the matching side in the first triangle.
  2. 2Since the three side ratios are equal, the triangles are similar.

Method you can reuse

  1. 1Match the corresponding vertices.
  2. 2Check equal angles or proportional sides.
  3. 3Compare in the same order.
  4. 4Conclude similarity only when the comparison is consistent.

Visual tip

No special diagram is needed, but matching vertices should be marked in the same order before writing ratios.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What must be true about corresponding angles and sides when two triangles are similar?

Think first, then show answer
If two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional. This means the triangles keep the same shape, even when the size changes.

Common wrong answer

Saying triangles are similar just because one side matches or because the sides are different. Similarity needs equal angles or proportional corresponding sides.

Don't mix this up

Students often think similar triangles must have equal side lengths. That is congruence, not similarity.

Exam tip

Write the corresponding vertices in the same order before checking angles or side ratios.

Similarity of triangles diagram

Open full screen to read every label clearly.

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

CBSE questions usually ask whether two triangles are similar from angle data, side ratios, or a short proof-based figure.
  1. 1

    Enough for 1 mark

    Two triangles are similar when their corresponding angles are equal and their corresponding sides are in the same ratio.

  2. 2

    Add for 2 marks

    Example: Triangles with sides 3 cm, 4 cm, 5 cm and 6 cm, 8 cm, 10 cm are similar because each matching side is in the ratio 1:2.

  3. 3

    Add for 3 marks

    Similarity means the triangles have the same shape, even if one is larger or smaller.

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