Question

1. given:

prove:

statement | reason

1. | 1. given
2. | 2.
3. | 3. vertical angles are congruent
4. | 4.
5. |

Explanation:

Step1: Identify the given information

1. $\overline{AE}\cong\overline{DE}$ (Given)
2. $\overline{BE}\cong\overline{CE}$ (Given)

Step2: Identify the vertical angles

1. $\angle BEA\cong\angle CED$ (Vertical angles are congruent)

Step3: Prove the triangles congruent

1. $\triangle BAE\cong\triangle CDE$ (By the Side - Angle - Side (SAS) congruence criterion: we have two pairs of congruent sides ($\overline{AE}\cong\overline{DE}$ and $\overline{BE}\cong\overline{CE}$) and the included angles ($\angle BEA\cong\angle CED$) are congruent)

Step4: Use the property of congruent triangles

1. $\angle BAE\cong\angle CDE$ (Corresponding parts of congruent triangles are congruent)

Answer:

1. Given
2. Given
3. $\angle BEA\cong\angle CED$
4. SAS (Side - Angle - Side)
5. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)