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gregori [183]
3 years ago
10

Explain why ΔABC cannot be shown to be congruent to ΔCDA.

Mathematics
1 answer:
igomit [66]3 years ago
4 0

There isn't enough info to prove the triangles to be congruent or not. So we can't say for sure either way.

We have angle CAD = angle ACB given by the arc markings, and we know that AC = AC due to the reflexive theorem. However we are missing one third piece of information.

That third piece of info could be....

  • AD = BC which allows us to use SAS
  • angle ACD = angle CAB which allows us to use ASA
  • angle ABC = angle CDA which allows us to use AAS (slight variation of ASA)

Since we don't know any of those three facts, we simply don't have enough information.

side note: If AB = CD, then this leads to SSA which is not a valid congruence theorem. If we had two congruent sides, the angle must be between the two sides, which is what AD = BC allows.

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