Question

PROOF: Given isosceles
with
, I can construct
, the angle bisector of
.Then, by the definition of an angle bisector, I know that
. I also know that linesegments are congruent to themselves, so
by the reflexive property of congruence. I nowhave two pairs of sides and an included angle that are congruent, so I know that
by the SAS Congruence Theorem.
What statement should be placed at the end of the proof?
(1 point)
△ABC AB ≅ ¯¯¯¯¯¯¯¯ BC ¯¯¯¯¯¯¯¯ BD
←→
∠B
∠ABD ≅∠CBD
BD ≅ ¯¯¯¯¯¯¯¯ BD ¯¯¯¯¯¯¯¯
△ABD ≅△CBD
Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so AB ≅ . ¯¯¯¯¯¯¯¯ BC ¯¯¯¯¯¯¯¯
Finally, ∠A ≅∠C by the Base Angles Theorem.
Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so ∠A ≅∠C.
Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so ∠A ≅∠B.

Answer 1

∠A ≅ ∠C

(From △ABD ≅ △CBD, corresponding parts of congruent triangles are congruent, so the base angles at A and C are equal.)