Question

Consider the following proof of the Base Angles Theorem. Which statement should fill in the blank?
PROOF: Given isosceles
with
, I can construct
, the midpoint of
. By thedefinition of a midpoint, I know that
. I can also construct
through points
and
.Because any line segment is congruent to itself by the reflexive property of congruence,
__________________________
. Corresponding parts of congruent triangles arecongruent by the CPCTC Theorem, so
.
(1 point)
△ABC AB ≅ ¯¯¯¯¯¯¯¯ BC ¯¯¯¯¯¯¯¯ D AC ¯¯¯¯¯¯¯¯
AD ≅ ¯¯¯¯¯¯¯¯ DC ¯¯¯¯¯¯¯¯ BD
←→
B D
BD ≅ ¯¯¯¯¯¯¯¯ BD ¯¯¯¯¯¯¯¯
∠A ≅∠C
I also know that △ABC ≅△ABC by the reflexive property of congruence
I also know that by the definition of an angle bisector, ∠ABD ≅∠CBD
I now have three pairs of sides congruent, so △ABD ≅△CBD by the SAS Congruence Theorem
I now have three pairs of sides congruent, so △ABD ≅△CBD by the SSS Congruence Theorem

Answer 1

BD ≅ BD