MHB Can triangles with the same side lengths have different angles?

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Triangles with the same side lengths are congruent, meaning they cannot have different angles. The discussion centers on triangle △ABC with side lengths 4, 4, and 7, which adheres to the Side-Side-Side (SSS) congruence criterion. Since congruent triangles have corresponding angles that are equal, no other triangle can exist with the same side lengths but different angles. Visual representations may aid understanding, but the underlying geometric principles confirm the conclusion. Therefore, triangles with identical side lengths must have identical angles.
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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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