This package on constructing and analyzing triangles using coordinate geometry, the distance formula, and the midpoint formula, is comprised of 4 activities.
The first 3 activities lead students through the construction of isosceles right, isosceles acute, and scalene obtuse triangles using coordinate geometry and graphing techniques. Students also calculate the lengths of sides of the triangles using the distance formula. Students also calculate the midpoints of the sides of the triangles using the midpoint formula.
The fourth activity walks students through the construction of the first few stages of a fractal (specifically, the Sierpinski triangle) using graphing techniques and coordinate geometry, including significant use of the midpoint formula. (Alternately, students could measure the lengths of the sides of the triangle using a ruler, and divide the lengths in half to find the midpoint of the line segment).
While the first 3 activities are straight forward, and could be completed in a full, single class period, the 4th activity is a bit time consuming and could be reserved for homework, or an in-class activity for honors-level students.
The last activity (the fractal) also makes use of the concept of congruent triangles.
Triangles and Coordinate Geometry
by Anthony J. Pultrone
is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License