Triangle Congruence Investigation

Caroline Psutka, ellen shermoen, Oct 17, 2023

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

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Copy of SSS - 3 pairs of congruent sides

Task
Your goal is to try everything to create a triangle that is NOT congruent to the completed triangle.
SSS CFU
Is it possible to create [math]\Delta[/math]PQR that is NOT congruent to[math]\Delta[/math] using the 3 side lengths given? [br][br]What does this result tell you?
– ellen shermoen, Caroline Psutka

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