Given two parallel lines, draw other lines that intersect the two parallel lines, forming various figures. Discuss the properties of the different polygons formed. Find as many properties of the figures as possible that hold whenever the intersecting lines are moved.
A diagonal of a polygon is created when two non-consecutive vertices are connected by a segment. In convex quadrilaterals, the diagonals can:
Find all of the possible combinations of diagonals that can occur and construct the quadrilateral that they define (p58-59 addm - geo)
Given any quadrilateral, construct a midpoint on each side. Connect each consecutive midpoint with a segment. What are the properties of the shape formed by joining the midpoints? Will this happen for any type of quadrilateral (e.g convex & concave)? How does the area of the new figure compare to the area of the original quadrilateral?