Can triangles with the same side lengths have different angles?

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SUMMARY

Triangles with the same side lengths are congruent, meaning they cannot have different angles. In the case of triangle ABC with side lengths 4, 4, and 7, any other triangle with these exact side lengths must also have the same angles. This conclusion is supported by the Side-Side-Side (SSS) congruence theorem and the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) principle, which establish that congruent triangles have identical angle measures.

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  • Understanding of the SSS congruence theorem
  • Knowledge of CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
  • Basic principles of triangle geometry
  • Familiarity with triangle properties and classifications
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  • Explore other triangle congruence theorems such as SAS and ASA
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akarikairi
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△ABC has side lengths 4, 4, and 7.
Is there another triangle with the same side lengths but different angles?

I get a lot of questions like these, and I don't know how to judge whether or not they are true or false. Drawing them on paper doesn't always help me either, but I do try to - to get a visual representation of the questions.
 
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Hi akarikairi,

If there was another triangle with the same side lengths, then by SSS the two triangles would be congruent. Then by CPCTC the corresponding angles are congruent. So there is no triangle with the same side lengths as ABC but with different angles.
 
Thank you for the explanation! This is very helpful.
 

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