Consider the following proof of the Base Angles Theorem. Which statement should fill in the blank?

Question

PROOF: Given isosceles △ABC with AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ , I can construct BD←→ , the angle bisector of ∠B . _____________________. I also know that line segments are congruent to themselves, so BD¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ by the reflexive property of congruence. I now have two pairs of sides and an included angle that are congruent, so I know that △ABD≅△CBD by the SAS Congruence Theorem. Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so ∠A≅∠C .

(1 point)
Responses

Then, by the definition of an isosceles triangle, I know that AB¯¯¯¯¯¯¯¯≅CA¯¯¯¯¯¯¯¯.
Then, by the definition of an isosceles triangle, I know that Modifying above upper A upper B with bar congruent to Modifying above upper C upper A with bar .

 Then, by the definition of a midpoint, I know that AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯.
 Then, by the definition of a midpoint, I know that Modifying above upper A upper D with bar congruent to Modifying above upper D upper C with bar .

Then, by the definition of an angle bisector, I know that ∠BAC≅∠BCA.
Then, by the definition of an angle bisector, I know that angle upper B upper A upper C congruent to angle upper B upper C upper A .

Then, by the definition of an angle bisector, I know that ∠ABD≅∠CBD.

Answer 1

The most appropriate statement to fill in the blank is:

Then, by the definition of an angle bisector, I know that ∠ABD≅∠CBD.

This statement logically follows from the previous context about constructing the angle bisector and is relevant to the proof's goal of demonstrating the base angles' congruence in an isosceles triangle.