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Triangle congruence and similarity criteria

Test your understanding of triangle congruence and similarity with a mixed set of geometry problems. You’ll decide which criteria apply (SSS, SAS, ASA, AAS, HL, AA, SAS~, SSS~) and justify conclusions...

119 Questions
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About this quiz

What you’ll practice

Triangle proofs get easier when you can quickly spot the right criterion. This quiz focuses on recognizing when triangles are congruent versus merely similar, and what that implies about corresponding parts.

You’ll work with classic criteria—SSS, SAS, ASA, AAS, and HL for congruence, plus AA, SAS~, and SSS~ for similarity—along with scale factors, proportional sides, and angle relationships.

Quiz format and difficulty

Each question has 4 options and there’s no timer, so you can reason carefully instead of rushing. Before you start, pick how many questions you want to answer and set the difficulty; “Mixed” blends straightforward identification items with multi-step reasoning.

To keep things fair, easier questions emphasize direct pattern recognition, while harder ones add extra markings, indirect information, or require choosing what you can (and cannot) conclude.

Common pitfalls to avoid

  • Mixing up congruence (same size/shape) with similarity (same shape, scaled)
  • Treating SSA as a valid congruence test (it usually isn’t)
  • Forgetting HL applies only to right triangles and needs hypotenuse + a leg
  • Assuming “looks equal” from a diagram instead of using given markings/labels
  • Using AA to claim congruence (AA proves similarity, not congruence)

Tips for better accuracy

Match corresponding vertices consistently before comparing sides/angles, and write proportions in the same order for both triangles. When a problem asks what must be true, focus on the minimum information required by the criterion, not extra facts that aren’t guaranteed.

Sample questions

Which criterion can be used to determine if two triangles are congruent if two sides and the included angle are known?

  • A.SAS
  • B.ASA
  • C.SSS
  • D.AAS

If two angles of one triangle are equal to two angles of another triangle, what can be concluded?

  • A.The triangles are similar
  • B.The triangles are congruent
  • C.The triangles have equal sides
  • D.The triangles are right triangles

What is the criterion for two triangles to be congruent if all three sides of one triangle are equal to all three sides of another triangle?

  • A.SSS
  • B.SAS
  • C.ASA
  • D.AAS

Quiz FAQ

How many questions are in this quiz?

This quiz has 119 questions on triangle congruence and similarity criteria.

Is this quiz timed?

No. Each question has 4 options and there is no timer, so you can work at your own pace.

What criteria are covered in the questions?

You’ll see SSS, SAS, ASA, AAS, and HL for congruence, plus AA, SAS~, and SSS~ for similarity.

How do I choose question count and difficulty?

Use the start panel to select how many questions you want and set the difficulty level; Mixed combines easy, medium, and hard items.

What’s a common mistake this quiz helps fix?

A frequent error is using SSA as a congruence test or using AA to claim congruence; the quiz drills the correct conclusions.

Play this quiz in another language(2)

sk
Kritériá kongruencie a podobnosti trojuholníkovSlovenčina
cs
Kritéria shody a podobnosti trojúhelníkůČeština

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