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Decide on which quadrilateral you will create. For this activity you may use a kite, trapezoid or a parallelogram (that is not a square, rhombus, or rectangle). Graph the quadrilateral on a coordinate plane. You may print and use graph paper a drawing program such as GeoGebra. The four vertices of the quadrilateral will serve as four destinations on your map. One can be the starting point, the others can be clues along the way, and the last one will be where X marks the spot! Find the length and slope of each side to justify the classification of your quadrilateral. For example, if your map was a square, your calculations would prove that all four sides are congruent, slopes of opposite sides are congruent, and slopes of adjacent sides are opposite reciprocals. You need to create a set of directions so you can come back and find the treasure later. Your directions need to explain how to get from each destination on the map to the next one. Use the properties of quadrilaterals in your directions. At least three different quadrilateral properties must be used. What does it mean to use properties of quadrilaterals in your directions? Here is an example: If your map is in the shape of a parallelogram, your opposite sides will have equal slopes. You could say that to get from Point A to Point B you travel up 3 units and right 2 units to the Palm Tree. From there you might travel East 5 units to Point C. From Point C, you would travel down 3 and left 2 units, where X marks the spot. This proves that the slopes of opposite sides are equal. Include two more properties in your directions. Don’t forget to finish the directions to return to the starting point. See example below. Get creative and think of clever ways to use the different properties! Create a key for your map. Show proof that following the directions will get you to the treasure. If one of the directions is to make a 90 degree turn, show how you can prove the turn from one side to another is 90 degrees. If one of the directions is to travel the same distance as a previous side, use the distance formula to show the two distances are the same.
Uff. This is a super long question. So choose the type of quadrilateral you want to draw, and draw one on the coordinate plane. If you're really struggling, how about this parallelogram with corners: (0,0), (10,0), (5,3), (5,13) Draw that and then try to work through the other questions.