Boutros' Geometry Questions - Oct. 17-21, 1994 For first period geometry, Boutros had to come up with some questions for a test that the students were writing based on the concepts they had learned in the first few weeks of class. He had come up with a few, but wasn't sure if they were any good. He shared them with Bernice on the way home, and asked her to answer them, and come up with a couple of her own. The list said: Can a plane intersect a circle in exactly two points? In exactly one point? What happens if the plane and the circle have three points in common? Can a plane intersect a triangle in exactly two points? In exactly one point? What happens if the plane and the triangle have three distinct points in common? Think of ways to put segments together to make a ray. How many segments will you need? Imagine an n-gon. If n = 4, what's the least number of triangles you can divide it into? If n = 5, what's the least number of triangles you can divide it into? If n = 6? n = 7? If you don't know n, can you write a formula to find the answer? Write your own question. [Much of this problem came from Clemens and Clemens, Geometry for the Classroom. ] Correct solutions to the problem were submitted by: Scott Hess, Shaler Area High School Micah Derr, Shaler Area High School Erik Ostrowski, Shaler Area High School Jennifer Abrahamsen, Fairfield HS Eric Wahl, Masterman Mount St. Joseph Academy Invented Questions from Fairfield HS Next problem || Previous problem || Table of Contents || Forum Home Page