Triangle congruence and similarity criteria

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.