Rayen Antillanca.
Assignment 6
Construct
the triangle with minimum perimeter inscribed in a given triangle.
The
inscribed triangle with minimum perimeter is constructed with the heights of
the original triangle.
Let ABC be any triangle 

First step
construct the heights 



Second
step, construct a new triangle joining the three bases of the heights 

Therefore, triangle DEF is the triangle with minimum perimeter 
To
prove that this triangle is the minimum perimeter you can draw another triangle
and compare these perimeters. The next GSP
file shows this.
Note: All figures on this web page were made with The Geometer’s
Sketchpad 