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A proof that uses arrows to show the flow of logic statements. ∠D. DF. ∠F. ∆DEF. ∠D. ∠F. EF. ∆DEF. sides. non-included. AAS Congruence Theorem. included. ASA Congruence Postulate. Statements. Reasons. ∠S ≅ ∠V. Given. Given. ∠STW ≅ ∠VWT. Reflexive Property. TW ≅ WT.
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A proof that uses arrows to show the flow of logic statements. ∠D DF ∠F ∆DEF
∠D ∠F EF ∆DEF
sides non-included AAS Congruence Theorem included ASA Congruence Postulate
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
supplementary supplementary Given supplementary Given ∠3 ∠ECF Reflexive Prop. AAS ≅ Theorem
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.
two angles included side ASA ≅ Postulate third vertex
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.