Breaking Up a Triangle - Feb. 20-24, 1995 Page and Jon sauntered into study hall. "Hey, Trey! We're suffering from chalk dust torture," said Page. "You got any of those problems we can work on to clear the brain?" "Sure thing," said Trey. "Just started working on this one this morning. Got a pencil? Take any triangle. Label it ABC. Construct D and E as the midpoints of BC and AB, respectively. Now construct DF and EF, where F is any point on AC. Now look at the triangles AEF and FCD and the quadrilateral BEFD. How are the areas of the triangles related to the area of the quadrilateral? What happens as F moves along AC? Can you explain why you think you're right?" "Shoot, Trey. Have you figured it out yet?" asked Jon. "Well, all things reconsidered, I think I'm doing okay, but I'm not done yet. Why don't you guys give it a try, and then we can talk about it?" Correct solutions to the problem were submitted by: David and Sarah McMenomy (home schooled), Bellevue, WA Emillia Ortiz, Westmont High School Kate Devine, Jen Hinke, Jordan Walsh, Mount St. Joseph Academy Joan Scott and Kate Devine, Mount St. Joseph Academy Susanna Puntel & Maria Szczesniak, Mount St. Joseph Academy 9th grade Geometry class, Wheatland Jr. High Next problem || Previous problem || Table of Contents || Forum Home Page