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.
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Let ABC be any triangle |
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First step
construct the heights |
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Second
step, construct a new triangle joining the three bases of the heights |
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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.
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Note: All figures on this web page were made with The Geometer’s
Sketchpad |