C
CraftExam
high importancemedium8 min

SSS similarity criterion

Two triangles are similar if all three corresponding sides are proportional.

Practice This Concept

Learn the concept

Student-friendly explanation

When every matching side ratio is the same, the triangle keeps the same shape and only the size changes. This is why three proportional sides are enough.

How to write this in exams

  1. 1

    Start with the exact idea

    Two triangles are similar if all three corresponding sides are proportional.

  2. 2

    Then show how to use it

    1. Arrange the corresponding sides. 2. Compare all three ratios. 3. If the ratios are equal, conclude similarity by SSS.

  3. 3

    Add one concrete example

    Sides 7 cm, 9 cm, 12 cm and 14 cm, 18 cm, 24 cm are proportional in the ratio 1:2, so the triangles are similar.

  4. 4

    Avoid this incomplete answer

    Saying similar after checking only two side ratios. SSS needs all three corresponding sides.

Definition

Two triangles are similar if all three corresponding sides are proportional.

Example

Sides 7 cm, 9 cm, 12 cm and 14 cm, 18 cm, 24 cm are proportional in the ratio 1:2, so the triangles are similar.

Rule to remember

SSS similarity: all three corresponding sides are proportional.

Memory hook

Three sides, one ratio.

Examples and method

Worked example

For triangles with sides 5, 12, 13 and 10, 24, 26, every ratio is 1:2. Therefore the triangles are similar by SSS.

Method to apply

1. Arrange the corresponding sides. 2. Compare all three ratios. 3. If the ratios are equal, conclude similarity by SSS.

Diagram support

Write the triangles in the same vertex order and mark matching sides before comparing ratios.

How CBSE asks it

A question may give only side lengths and ask whether similarity can be proved without angle information.

Avoid common mistakes

Common confusion

Students sometimes check only two side ratios or mix up the side order.

Common wrong answer

Saying similar after checking only two side ratios. SSS needs all three corresponding sides.

Exam tip

Always compare sides in matching order before concluding SSS similarity.

Quick check

What condition must be satisfied to use SSS similarity between two triangles?

SSS similarity is used when all three corresponding sides are proportional in the same order. If the three ratios match, the triangles are similar.

Answer writing and exam use

1-mark answer

Two triangles are similar if all three corresponding sides are proportional.

2-mark answer

Two triangles are similar if all three corresponding sides are proportional. SSS similarity: all three corresponding sides are proportional. Sides 7 cm, 9 cm, 12 cm and 14 cm, 18 cm, 24 cm are proportional in the ratio 1:2, so the triangles are similar.

3-mark answer

When every matching side ratio is the same, the triangle keeps the same shape and only the size changes. This is why three proportional sides are enough. SSS similarity: all three corresponding sides are proportional. For triangles with sides 5, 12, 13 and 10, 24, 26, every ratio is 1:2. Therefore the triangles are similar by SSS. A question may give only side lengths and ask whether similarity can be proved without angle information. Saying similar after checking only two side ratios. SSS needs all three 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