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Rowena is proving that ad ≅ eb. Which statement does the ♣ represent in her proof?

1) Δacd ≅ Δecb
2) Δacd ≅ Δefd
3) Δafb ≅ Δefd
4) Δafb ≅ Δecb

1 Answer

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Final answer:

The '♣' in Rowena's proof to establish that AD ≅ EB likely represents the statement ΔACD ≅ ΔECB, as corresponding parts of congruent triangles are congruent (CPCTC).

Step-by-step explanation:

Rowena is proving that AD ≅ EB. The statement that the '♣' represents in her proof must be linked to congruent triangles, as congruent corresponding parts of congruent triangles are congruent (CPCTC). Now, consider that AD is a part of △ACD and EB is a part of △ECB. The most logical choice to show that AD ≅ EB would be to prove that △ACD ≅ △ECB. If these triangles are congruent, then their corresponding sides (AD from △ACD and EB from △ECB) must be congruent. This reasoning leads us to conclude that the statement represented by the '♣' must be option (1): △ACD ≅ △ECB.

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