Triangle Congruence Investigation

Caroline Psutka, Bailey Newell, 09/set/2025

What consecutive triangle parts need to be congruent in order to show that two triangles are congruent? These applets allow students to explore whether triangle relationships (SSS, AAA, SAS, HL, SSA, ASA, AAS) force triangles to be congruent or not. Are you able to create a non-congruent pair of triangles?


  • 1. SSS - 3 pairs of congruent sides
  • 2. SAS- 2 Congruent Sides with Congruent Angle in Between
  • 3. ASA- 2 Pairs of Congruent Angles with a Congruent Side in between
  • 4. AAS- 2 Pairs of Congruent Angles with a Congruent Side NOT inbetween
  • 5. AAA- 3 pairs of congruent angles
  • 6. HL- 1 Pair of Legs Congruent, 1 Pair of Hypotenuses Congruent, ONLY for right triangles
  • 7. SSA- 2 Congruent Sides with a Congruent Angle NOT in between

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SSS - 3 pairs of congruent sides

– Caroline Psutka

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