Use what you have learned about slope to calculate the slope of each side. Use what you have learned about distance (use Pythagorean Theorem! a^2+b^2=c^2) to find the length of each side and the length of each diagonal. Use the online dynamic geometry sketch to explore the angles of the quadrilaterals as well as to verify the lengths you have found.
For each quadrilateral, answer the following questions. 1) How are the opposite sides related? (slope and length) 2) How are the opposite angles related? Consecutive angles? (measurement) 3) What are the lengths of the diagonals of each quadrilateral? How does the point of intersection divide the diagonals? When the diagonals are drawn in, what can you conclude about the angles created? 4) What can you conclude about the angles created by the diagonals around the intersection point? 5) Write as many general statements about each quadrilaterals as you can. Use key words like: parallel, opposite, consecutive, congruent, bisects, etc. Based on Section 5-4, what type of quadrilateral is ABCD, EFGH, IJKL, and MNOP? Do you see any similarities or differences between quadrilaterals ABCD, EFGH, IJKL, and MNOP? If so, what are they? Do you see any relationships between quadrilaterals ABCD, EFGH, IJKL, and MNOP? If so, what are they? Remember: Lines with the same slope are parallel. Lines with slopes that are negative reciprocals of each other are perpendicular. Perpendicular lines form right angles. Opposite sides (or angles) are across from each other. Consecutive sides (or angles) are next to each other.