Geometrica ! (reformat)

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JWOK GEOMETRY

Geometrica Fights Back ! ! ! ! Mystery of the Guilty Quadrilateral

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nce upon a time long, long ago in a far, far away land known as Geometrica there occurred an unspeakable crime. On a dark and dreary night as the Circular family lay sleeping in their soft, round beds and dreaming of their favorite dessert, pi, a violent criminal murdered them. Their neighbor, Mrs. Equi Angular said that she and her husband, Mr. Tri Angular, heard the awful blood curdling screams. So, they sprang from their bed to see what was the matter, and what to their wandering eyes did appear (not eight tiny reindeer) but a strange four-sided figure leaping from the Circular’s upstairs window. Well, the Angulars gave a description of the terrible beast and so did many other Geometrica residents. However, to this day, the mystery remains. Therefore, Detective Pentagonal Walsh of Geometrica’s Most Wanted has asked for your assistance in solving this crime. Below you will find descriptions that tipsters have given the authorities. Your job is to list the suspects from your line-up of twelve that meet each set of criteria. Use the dossier (a file containing detailed records on a particular person or subject) provided to analyze each of the suspects and look for their identifying information to make your decisions. You may use a GeoTool for measurements of angles and sides. Do not share with other investigation teams, as there is a reward for the team that captures the killer. Rumor has it that the Circular family has a special collection of valuable ancient coins! ! ! ! 1. Four-sided figure and convex Suspects:________________________________________ 2. Four-sided figure with two sets of parallel sides Suspects:________________________________________ 3. Four-sided figure with four right angles Suspects:________________________________________ 4. Four-sided figure with all sides equal Suspects:________________________________________ 5. Four-sided figure whose diagonals bisect each other Suspects:________________________________________ 6. Four-sided figure whose opposite angles are congruent Suspects:________________________________________ 7. Four-sided figure with only one set of parallel sides Suspects:________________________________________ 8. Four-sided figure whose consecutive angles are supplementary JWOK 1

Suspects:________________________________________ 9. Four-sided figure whose diagonals are congruent Suspects:________________________________________ 10. Four-sided figure whose diagonals are perpendicular Suspects:________________________________________ 11. Four-sided figure with all equal sides and four right angles Suspects:________________________________________ 12. Four-sided figure with all equal sides and perpendicular diagonals Suspects:_________________________________ 13. Four-sided figure with all equal sides and congruent diagonals Suspects:________________________________________ 14. Four-sided figure whose legs are congruent Suspects:________________________________________ 15. Four-sided figure whose opposite sides are congruent Suspects:________________________________________ 16. Four-sided figure and concave Suspects:________________________________________ 17. Four-sided figure with exactly one pair of opposite angels that are congruent Suspects:__________________________ 18. Four-sided figure with no parallel sides Suspects:________________________________________ 19. Four-sided figure with two right angles Suspects:________________________________________ 20. Four-sided figure with no equal sides (scalene) Suspects:________________________________________ 21. Suspect might be a parallelogram. JWOK 2

Suspects:________________________________________ 22. Suspect might be a trapezoid. Suspects:________________________________________

Who killed the Circulars? The guilty quad is the one whose number appears the most in the list above. Suspect number ____________ is the criminal. PROOF: Number of times that he appears? _________________________________________ PROOF: Reports in which he appears? _________________________________________ On the sheet of poster board provided, have your group draw a reproduction of the quadrilaterals family tree, complete with family portraits of each family member. In the bottom right corner, draw a mug shot of the quad that you found guilty of murder. Be sure to show/draw all information about each family member using the information found in your dossier. Use correct mathematical symbols and be creative! ! !

JWOK 3