Short Answer 
The process involves identifying corresponding angles between parallel lines, establishing that triangles formed by these angles are similar due to angle congruence, and applying mathematical methods like compendo and dividendo to prove the relationships between them.
Step 1: Identify Corresponding Angles
First, recognize that when dealing with two parallel lines (BD and AE), the corresponding angles are important. For instance, angle 4 is equal to angle 1, and angle 3 is equal to angle 2. This is based on the property of parallel lines intersected by a transversal, where corresponding angles remain congruent.
Step 2: Establish Similar Triangles
Next, analyze the triangles formed by these angles. Since triangle AED is parallel to triangle BDE, you can conclude that the sides of these triangles will be proportional. This proportionality arises from the angles being equal, leading us to verify that the triangles share similar characteristics based on their angle congruence.
Step 3: Apply Compendo and Dividendo
Finally, utilize the methods of compendo and dividendo to prove your results. By manipulating the proportions established from corresponding angles and the triangles, you’ll derive the desired conclusions about their relationships. This mathematical process effectively integrates the properties of angles and triangles to affirm your findings.