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igomit [66]
3 years ago
13

List all 6 Congruence statements for the following triangles.

Mathematics
1 answer:
Lera25 [3.4K]3 years ago
5 0

Answer:

Side side side

angle side angle

Hypotenuse leg

side angle side

CPCTC

ANGLE ANGLE SIDE

Step-by-step explanation:

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1:2

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Explain in your own words how you determine what the cooresponding parts are of a
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Explain why ΔABC cannot be shown to be congruent to ΔCDA.
igomit [66]

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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