Column Proof Triangle Congruence

Given

$$\overline{KM}\cong\overline{MK}$$

Definition of Congruent Segments

Prove

<BCA=<DCE because they are vertical angles and vertical angles are always congruent to each other

<C=<C because they are vertical angles and vertical angles are always congruent to each other

<EDC=<ACB because they are vertical angles and vertical angles are always congruent to each other

None of the above; we don't actually have vertical angles

HA=HA

HA=AH

MA=AM

MA=MA

∆HFG≅∆IHF

∆FHG≅∆IHF

∆GFH≅∆IFH

∆HFG≅∆IFH

∠ABC≅∠EDC

∠BCA≅∠DCE

BC≅CD

∠E≅∠A

∡EDA≅∡DCB

∡AED≅∡BEC

DE=CE

∡AED≅∡CED

Transitive Property, SAS (Side-Angle-Side)

Reflexive Property, SAS (Side-Angle-Side)

Reflexive Property, Vertical Angles Theorem

Transitive Property, SSS (Side-Side-Side)

BC≅DC

AC≅EC

BC≅DC, AC≅EC

∆BCA≅∆DCE