Thales’ Theorem
Thales was a Greek mathematician who lived in 654-625 BC. He was considered by many as the first mathematician. One of his famous achievements was devising the first formal geometric proof. The theorem he proved is what is now known as Thales’ Theorem.
The Theorem
Thales’ Theorem states that if 
, 
, and 
are points on the circle, and 
is a diameter, then angle 
a right angle.You should explore this by drawing circles and different sizes and drawing the triangle. You may also want to use a dynamic software.
The Proof
The proof of Thales’ Theorem is quite easy. First, we draw line segment 
to form two isosceles triangles 
and 
. Now, the base of the isosceles triangles are congruent as indicated by 
and 
in the second figure. The sum of the interior angles of a triangle 
is 
. So,
.
Simplifying, we have 
Dividing both sides by 2, we have 
But 
is the measure of angle .
Therefore, the measure of angle is 
. And we are done.
09. October 2012 by Guillermo Bautista
Categories: Geometry, Grades 6-8, HS Math |
Tags: thales' theorem, triangle angle sum |
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