 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 1, Part C:
Folding Paper

In This Part: Constructions | Constructing Triangles | Concurrencies in Triangles
More Constructions

When three or more lines meet at a single point, they are said to be concurrent. The following surprising facts are true for every triangle:

 The medians are concurrent; they meet at a point called the centroid of the triangle. (This point is the center of mass for the triangle. If you cut a triangle out of a piece of paper and put your pencil point at the centroid, you would be able to balance the triangle there.)  The perpendicular bisectors are concurrent; they meet at the circumcenter of the triangle. (This point is the same distance from each of the three vertices of the triangles.)  The angle bisectors are concurrent; they meet at the incenter of the triangle. (This point is the same distance from each of the three sides of the triangles.)  The altitudes are concurrent; they meet at the orthocenter of the triangle.  Triangles are the only figures where these concurrencies always hold. (They may hold for special polygons, but not for just any polygon of more than three sides.) We'll revisit these points in a later session and look at some explanations for why some of these lines are concurrent. You'll explore the derivation of such terms as incenter and circumcenter later in Session 5 of this course.      Problem C5 For each construction in parts a-d, start with a freshly drawn segment on a clean piece of patty paper. Then construct the following shapes:

 a. an isosceles triangle with your segment as one of the two equal sides b. an isosceles triangle whose base is your segment c. a square based on your segment d. an equilateral triangle based on your segment    Session 1: Index | Notes | Solutions | Video