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Arrow Flow Proof: AAS Congruence Theorem and Side Logic

This proof uses arrows to demonstrate the logical flow of statements regarding angles, triangles, and congruence. It showcases the application of AAS Congruence Theorem, ASA Congruence Postulate, and the logic behind angles and triangle sides. By showcasing the flow of logic through arrows, this proof helps in understanding geometric congruence principles effectively.

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Arrow Flow Proof: AAS Congruence Theorem and Side Logic

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  1. A proof that uses arrows to show the flow of logic statements. ∠D DF ∠F ∆DEF

  2. ∠D ∠F EF ∆DEF

  3. sides non-included AAS Congruence Theorem included ASA Congruence Postulate

  4. Statements Reasons ∠S ≅ ∠V Given Given ∠STW ≅ ∠VWT Reflexive Property TW ≅ WT AAS ≅ Theorem ∆STW ≅ ∆VWT Statements Reasons ∠SWT ≅ ∠VTW Given ∠STW ≅ ∠VWT Given TW ≅ WT Reflexive Property AAS ≅ Postulate ∆STW ≅ ∆VWT

  5. supplementary supplementary Given supplementary Given ∠3 ∠ECF Reflexive Prop. AAS ≅ Theorem

  6. CF bisects ∠BFD CF bisects ∠ACE Given Given ∠ACF ≅ ∠ECF ∠BFC ≅ ∠DFC CF ≅ CF Def. of ∠ bisector Def. of ∠ bisector Reflexive Prop. ∆CBF ≅ ∆CDF ASA ≅ Post.

  7. two angles included side ASA ≅ Postulate third vertex

  8. The triangle formed is unique according to the AAS congruence theorem. Therefore, one actor cannot move without requiring the spotlight to also move and changing the triangle.

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