Write a two-column proof. Given: line BD bisects angle CBE. Prove: angle ABD approximately equal to angle FBD.

The proof is derived from the summarily following equations;

∠FBE + ∠EBD = ∠CBA + ∠CBD

∠FBE + ∠EBD = ∠FBD

∠CBA + ∠CBD = ∠ABD

Therefore;

∠ABD ≅ ∠FBD

Step-by-step explanation:

The two column proof is given as follows;

Statement                                       Reason          

bisects ∠CBE                            Given

Therefore;

∠EBD ≅ ∠CBD                                Definition of angle bisector

∠FBE ≅ ∠CBA                                Vertically opposite angles are congruent

Therefore, we have;

∠FBE + ∠EBD = ∠CBA + ∠CBD     Transitive property

∠FBE + ∠EBD = ∠FBD                    Angle addition postulate

∠CBA + ∠CBD = ∠ABD                   Angle addition postulate

Therefore;

∠ABD ≅ ∠FBD                                  Transitive property.

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step-by-step explanation: