Alternate Exterior Angles Theorem
If a transversal intersects two parallel lines, then the alternate exterior angles are congruent.
Converse also true:
If a transversal intersects two lines and the alternate exterior angles are congruent, then the lines are parallel.
Two triangles are similar if and only if the corresponding sides are in proportion and the corresponding angles are congruent.
If a line is parallel to one side of a triangle and intersects the other two sides of the triangle, the line divides these two sides proportionally
If MBP is any triangle and LA is drawn parallel to MB, then PL/CE = PA/CE
A general example to help you recognize patterns and spot the information you're looking for
Alternate exterior angles and same side interior angles are involved in the construction of buildings and bridges...
They are mostly used in engineering, architecture, and construction and can be used in scale drawings and finding distance height of the buildings.