Question

deltamath
back to home
triangle proofs
no late credit
grade: 0%
complete: 52%
interior and exterior triangle angles
triangle congruence criteria
triangle congruence, basic flowchart proof
triangle congruence, flowchart proof (level 1)
scientific calculator
graphing calculator
don dorsey
log out
\\(\overline{ae}\cong\overline{ec}\\) reason: select reason
\\(\overline{be}\cong\overline{ed}\\) reason: select reason
\\(\angle bea\cong\angle ced\\) reason: select reason
\\(\triangle abe\cong\triangle cde\\) reason: select reason

Explanation:

Step1: Identify given information

We are given that $\overline{AE}\cong\overline{EC}$ and $\overline{BE}\cong\overline{ED}$ and $\angle BEA\cong\angle CED$.

Step2: Recall congruence criteria

The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In $\triangle ABE$ and $\triangle CDE$, $\overline{AE}\cong\overline{EC}$, $\angle BEA\cong\angle CED$ (the included angle) and $\overline{BE}\cong\overline{ED}$.

Answer:

• $\overline{AE}\cong\overline{EC}$ Reason: Given
• $\overline{BE}\cong\overline{ED}$ Reason: Given
• $\angle BEA\cong\angle CED$ Reason: Vertical angles are congruent
• $\triangle ABE\cong\triangle CDE$ Reason: Side - Angle - Side (SAS) congruence criterion