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 AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯
.
Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so Modifying above upper A upper B with bar congruent to Modifying above upper B upper C with bar .
Finally, ∠A≅∠C
by the Base Angles Theorem.
Finally, angle upper A congruent to angle upper 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 angle upper A congruent to angle upper C .
Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so ∠A≅∠B
.
1 answer
The most appropriate statement to place at the end of the proof is:
"Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so ∠A≅∠C."
This concludes the proof by establishing that the angles at the base of the isosceles triangle (angles A and C) are congruent, supporting the property of isosceles triangles that their base angles are equal.
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