Inscribed Quadrilateral

by

Tennille Rushin

 

Problem:  To prove that opposite angles of an inscribed quadrilateral are supplementary.

 

First construct a circle.

 

 

 

 

 

 

 

 

Then add four points on the circle and create an inscribed quadrilateral.

 

 

 

Construct a segment AC.  This will create two triangles. 

 

Measure angle DAB and angle BCD.

Angle DAB and BCD added up to 180 degrees proving they are supplementary angles.  Angle DAB is 1/2 of arc BCD and angle BCD is 1/2 of arc BAD.  In conclusion anytime you have an inscribed quadrilateral, (inside the circle), opposite angles will be supplemental.

 

inscribedquadrilateral

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