Thales Theorem

Thales theorem: Let A,B,C be points on a circle. Let AB be the Diameter of the circle. Then ACB is a right angle. Screen Shot 2014-05-27 at 6.16.03 PM Proof: Let x be angle DAC. Since DA and DC are the radius of the circle they have the same length. It follows, that DAC has the same angle as DCA. Let DBC be y. We can use the same argument to show that DCB has the angle y. Since the sum of all angles in a triangle is 180 degrees, BDC is 180-2y and ADC is 180-2x. If we add these Angles we get 180 degrees since A,D,B lie on one line. We add all angles in both triangles. 180-2x+180-2y+2x+2y=360. 180+2x+2y=360. 2x+2y=180. Now we divide by 2 on both sides: x+y=90. This completes the proof since x+y is the size of the angle ACB.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s