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Triangles e f g and e prime f prime g prime are shown. angles f e g and f prime e prime g prime are 72 degrees. angles e f g and e prime f prime g prime are 66 degrees. what additional information could be used to prove ?efg ?e'f'g' using aas? check all that apply. eg = 12 and e'g' = 12 fg = 15 and f'g' = 15 ef = 10 and e'f'= 12 m?g = 42� and m?g' = 42� eg ? e'g'

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Final Answer:

Additional information that could be used to prove △EFG ≅ △E'F'G' using AAS is eg = 12 and e'g' = 12.

Step-by-step explanation:

In the given triangles △EFG and △E'F'G', the angles ∠FEG and ∠F'E'G' are given as 72°, while ∠EGF and ∠E'G'F' are 66°. To establish congruence using the AAS criterion, we require one more pair of corresponding equal angles. Selecting the information eg = 12 and e'g' = 12 becomes crucial for this proof.

By employing the Side-Angle-Side (SAS) congruence criterion, we can now show that △EFG ≅ △E'F'G'. The angles ∠FEG and ∠F'E'G' serve as the angle components, and the sides EG and E'G', being equal in length (eg = e'g' = 12), constitute the side component. This fulfills the conditions for the AAS congruence, as both triangles share an equal side and a pair of corresponding equal angles.

Other provided options do not offer a complete set of conditions for proving AAS congruence. Equal side lengths alone, as in fg = 15 and f'g' = 15, are insufficient without a corresponding pair of equal angles. Likewise, having equal angles or approximately equal sides does not satisfy the AAS congruence criteria. Therefore, the specified information, eg = 12 and e'g' = 12, uniquely satisfies the AAS conditions and allows us to conclude that △EFG ≅ △E'F'G'.

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