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 h ave 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 traingles are congruent by the CPCTC theorem, so <A = <C.
a. then, by the definition of a midpoint, i know that AD = Dc.
b. the, by the definition of an angle bisector, i know that <BAC = <BCA
c. then, by the definition of an isosceles triangle, i know that AB = CA
d. then, by the definition of an angle bisector, i know that <ABD = <CBD
1 answer
In the context of the proof for the base angles theorem, the correct statement to fill in the blank is:
d. then, by the definition of an angle bisector, i know that <ABD = <CBD
This statement properly links the construction of the angle bisector BD with the angle measurements, leading to the conclusion about the congruence of triangles ABD and CBD and ultimately proving that the angles A and C are equal.
