Question

C is the incenter of isosceles triangle abd with vertex angle ∠abd. Does the following proof correctly justify that triangles abc and dbc are congruent?

1) Yes, because the incenter of a triangle is equidistant from the three sides of the triangle.
2) No, because the incenter of a triangle is not necessarily equidistant from the three sides of the triangle.
3) Cannot be determined based on the given information.

Answer 1

The proof does not correctly justify that triangles ABC and DBC are congruent because the incenter of a triangle is not necessarily equidistant from the three sides of the triangle. Hence the correct answer is option 2

Step-by-step explanation:

The proof does not correctly justify that triangles ABC and DBC are congruent. The statement in option 1 is incorrect. The incenter of a triangle is not necessarily equidistant from the three sides of the triangle. Option 2 correctly states that the incenter of a triangle is not necessarily equidistant from the three sides.

Therefore, the answer is 2) No, because the incenter of a triangle is not necessarily equidistant from the three sides of the triangle.