Geometrica Fights Back
Mystery of the Guilty Quadrilateral
Once 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.
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
Suspects:______
9. Four-sided figure whose diagonals are congruent
Suspects:______
10. Four-sided figure whose diagonals are perpendicularSuspects:______
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 congruentSuspects:______
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.
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 above list.
Suspect number ______is the criminal.