Question

consider the following proof of the base angles theorem. which statement should fill in the blank? proof: given isosceles △abc with (overline{ab}congoverline{bc}). i can construct (overrightarrow{bd}), the angle - bisector of (angle b). ____________ i also know that line segments are congruent to themselves, so (overline{bd}congoverline{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 (angle acongangle c). (1 point) then, by the definition of a mid - point, i know that (overline{ad}congoverline{dc}) then, by the definition of an angle bisector, i know that (angle abdcongangle cbd) then, by the definition of an angle bisector, i know that (angle baccongangle bca) then, by the definition of an isosceles triangle, i know that (overline{ab}congoverline{ca})

Explanation:

Step1: Recall angle - bisector property

Since \(BD\) is the angle - bisector of \(\angle B\), by the definition of an angle - bisector, \(\angle ABD=\angle CBD\).

Answer:

Then, by the definition of an angle - bisector, I know that \(\angle ABD\cong\angle CBD\)