Question

Use the image and the proof of the Base Angles Theorem to answer the question.

An isosceles triangle is marked clockwise from the lower left vertex as upper A upper B upper C. The sides upper A upper B and upper B upper C are marked with single congruent tick marks.

PROOF: Given isosceles △ABC
with AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯
, I can construct BD←→
, the angle bisector of ∠B
. Then, by the definition of an angle bisector, I know that ∠ABD≅∠CBD
. 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.

What statement should be placed at the end of the proof?

(1 point)
Responses

 Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so ∠A≅∠B
.
 Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so angle upper A congruent to angle upper B .

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 angle upper A congruent to angle upper C .

Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯
.
Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so line segement upper A upper B congruent to line segement upper B upper C .

Finally, ∠A≅∠C
by the Base Angles Theorem.

Answer 1

Finally, corresponding parts of congruent triangles are congruent (CPCTC), so ∠A ≅ ∠C.