You can find the interior angle measures in a regular polygon and then use what you know about triangles and special quadrilaterals to analyze complex figures.
ABCDEF is a regular hexagon. What is the most precise classification of quadrilateral GBHE? How do you know? What are the interior angle measures of GBHE?
JKLM is a parallelogram. If you extend each side by a distance x, what kind of quadrilateral is PQRS? How do you know?
You can use coordinates and certain relationships between pairs of corresponding parts to prove triangles congruent in the coordinate plane.
What are two methods for proving the two triangles congruent? Use one of your methods along with coordinate geometry to prove that the two triangles are congruent.