Question

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

Answer 1

Answer:

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          

$\underset{BD}{\rightarrow}$ 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.