C
CraftExam
high importancemedium8 min

Similarity of triangles

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

Practice This Concept

Learn the concept

Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete 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.

  4. 4

    Avoid this incomplete answer

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

Definition

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

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.

Rule to remember

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

Memory hook

Same shape, different size.

Examples and method

Worked example

For 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. Since the three side ratios are equal, the triangles are similar.

Method to apply

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

Diagram support

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

How CBSE asks it

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

Avoid common mistakes

Common confusion

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

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.

Exam tip

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

Quick check

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

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.

Study the similarity of triangles diagram carefully

Use the labelled diagram to keep similarity of triangles clear in short answers and revision.

What this diagram makes clear

This diagram keeps the labels and direction of similarity of triangles in the right order.

Where this helps in exams

Use this for labelled diagram work and short exam answers on similarity of triangles.

Revision cue

Revise similarity of triangles through the labels before writing the answer.

Answer writing and exam use

1-mark answer

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

2-mark answer

Two triangles are similar when their corresponding angles are equal and their corresponding sides are in the same ratio. Corresponding angles are equal, and corresponding sides are proportional in similar triangles. 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-mark answer

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. Corresponding angles are equal, and corresponding sides are proportional in similar triangles. For 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. Since the three side ratios are equal, the triangles are similar. CBSE questions usually ask whether two triangles are similar from angle data, side ratios, or a short proof-based figure. Saying triangles are similar just because one side matches or because the sides are different. Similarity needs equal angles or proportional corresponding sides.
MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results
Practice This Concept

Help improve this page

Found something confusing, incorrect, or missing?

Practice This Concept