Question

based on the given diagram, prove \\( \triangle abe \cong \triangle cde \\) by filling out the flowchart below.
for each box, choose a statement format from the dropdown menu. you will then be able to change the letters to match the diagram for this problem.
\\( \overline { b a e } \cong \overline { c } \\)
reason:
reflexive
property
type of statemen
reason:
type of statemer
reason:

Explanation:

Step1: Identify vertical angles

$\angle AEB\cong\angle CED$ (Vertical Angles Theorem: vertical angles are congruent)

Step2: Identify side - side - side (SSS) or side - angle - side (SAS) components

We know that $BE = DE$ (marked as equal in the diagram) and $AE=CE$ (marked as equal in the diagram). Also, from Step 1, $\angle AEB\cong\angle CED$. So, by the Side - Angle - Side (SAS) congruence criterion:
If in two triangles, two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent.
For $\triangle ABE$ and $\triangle CDE$:

• $AE = CE$ (given by the marks on the diagram)
• $\angle AEB=\angle CED$ (vertical angles)
• $BE = DE$ (given by the marks on the diagram)

Answer:

$\triangle ABE\cong\triangle CDE$ by the SAS (Side - Angle - Side) congruence criterion.