QuestionGiven: $\overline{B E} \cong \overline{B D}$ and $\angle A B E \cong \angle C B D$. Prove: $\triangle A B C$ is an isosceles triangle.
Step
1 try Type of Statement $\angle A B E \cong \angle C B D$ Given
Reason
Given

Studdy Solution
Statement: $\triangle ABC$ is an isosceles triangle Reason: Definition of Isosceles Triangle Explanation: We have proven that $\overline{AB} \cong \overline{BC}$ (since $\overline{AB} = \overline{AD} + \overline{DB}$ and $\overline{BC} = \overline{EC} + \overline{DB}$, and we know $\overline{AD} \cong \overline{EC}$ and $\overline{DB} \cong \overline{DB}$). An isosceles triangle is defined as a triangle with at least two congruent sides.
Therefore, we have proven that $\triangle ABC$ is an isosceles triangle.