C is the centroid of isoceles triangle ABD with vertex angle <ABD. Does the following proof correctly justify that triangles ABE and DBE are congruent?

1. It is given that triangle ABD is isoceles, so segment AB is congruent to DB by the definition of isoceles triangle.
2. Triangles ABE and DBE share side BE. so it is congruent to itself by the reflexive property.
3. It is given that C is the centroid of triangle ABD, so segment BE is a perpendicular bisector.
4. E is a midpoint. creating congruent segments AE and DE, by the definition of midpoint.
5. Triangles ABE and DBE are congruent by the SSE postulate.

ANSWER CHOICES:
○ There is an error in line 1; segment AB and BC are congruent.
○ There is an error in line 2; segment BE is not a shared side.
○ There is an error in line 3; segment BE should be a median.
○ The proof is correct.

The centroid is the point where the three medians of the triangle intersect. It has the following properties: The centroid is always located in the interior of the triangle. The centroid is located 2/3 of the distance from the vertex along the segment that connects the vertex to the midpoint of the opposite side.

Which angles are congruent in the isosceles triangle?

Isosceles triangles have at least two congruent sides and at least two congruent angles. The congruent sides, called legs, form the vertex angle. The other two congruent angles are the base angles.

Learn more about centroid here: brainly.com/question/1515689

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