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Congruence criteria: Class 7 practice

Two triangles are congruent if they match by SSS, SAS (included angle), ASA, AAS or RHS (right angle–hypotenuse–side). Read the method, follow the three worked examples, then try the six questions.

What you should know first

  • Triangles

The idea behind congruence criteria

Two triangles are congruent if they match by SSS, SAS (included angle), ASA, AAS or RHS (right angle–hypotenuse–side). SSA and AAA do not guarantee congruence.

Step-by-step method

  1. List the equal parts.
  2. Check whether an angle is between the two sides (SAS).
  3. Name the criterion, or say none applies.

Worked example 1 (Basic)

△ABC and △PQR have two angles and a non-included side equal (e.g. sides 9 cm, 4 cm, angle 46°). Which congruence rule applies?

  1. Match the given parts to a rule
  2. Answer: AAS

Worked example 2 (Standard)

△ABC and △PQR have two angles and the side between them equal (e.g. sides 7 cm, 6 cm, angle 98°). Which congruence rule applies?

  1. Match the given parts to a rule
  2. Answer: ASA

Worked example 3 (Challenge)

△ABC and △PQR have three pairs of sides equal (e.g. sides 7 cm, 9 cm, angle 82°). Which congruence rule applies?

  1. Match the given parts to a rule
  2. Answer: SSS

Common mistakes and misconceptions

  • Using SSA
  • Using AAA (only similar)

Practice questions

  1. (Basic) △ABC and △PQR have two sides and a non-included angle equal (e.g. sides 4 cm, 12 cm, angle 47°). Which congruence rule applies?
  2. (Basic) △ABC and △PQR have three pairs of sides equal (e.g. sides 9 cm, 11 cm, angle 51°). Which congruence rule applies?
  3. (Standard) △ABC and △PQR have two angles and a non-included side equal (e.g. sides 10 cm, 6 cm, angle 35°). Which congruence rule applies?
  4. (Standard) △ABC and △PQR have two sides and a non-included angle equal (e.g. sides 9 cm, 12 cm, angle 63°). Which congruence rule applies?
  5. (Challenge) △ABC and △PQR have all three angles equal (e.g. sides 8 cm, 10 cm, angle 39°). Which congruence rule applies?
  6. (Challenge) △ABC and △PQR have two angles and the side between them equal (e.g. sides 6 cm, 12 cm, angle 38°). Which congruence rule applies?

Answer key with full working

  • Q1: Match the given parts to a rule → Answer: Not enough (SSA)
  • Q2: Match the given parts to a rule → Answer: SSS
  • Q3: Match the given parts to a rule → Answer: AAS
  • Q4: Match the given parts to a rule → Answer: Not enough (SSA)
  • Q5: Match the given parts to a rule → Answer: Not enough (AAA gives similar, not congruent)
  • Q6: Match the given parts to a rule → Answer: ASA

Syllabus note

This skill is listed under "Congruence of Triangles" for Class 7 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Related practice and notes

Frequently asked questions

Which chapter is congruence criteria in?

"Congruence of Triangles", Class 7 Maths (NCERT/CBSE). Other boards may place it differently.

How were the answers checked?

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

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