Basic Geometric Proofs

 

 

Claim:

Let A, B, C, D be points on a circle where A is not equal to B, and C is not equal to D. Suppose that lines AB and CD intersect at a point P. Then (PA) (PB) = (PC) (PD).

 

GSP Sketch and Proof

 

Claim:

If a quadrilateral has a circle inscribe in it, then the sum of one pair of opposite sides is equal to the sum of the other pair of opposite sides.

 

GSP Sketch and Proof

 

Claim:

For every quadrilateral, the midpoints of its sides form the vertices of a parallelogram.

 

GSP Sketch and Proof

 

Claim:

Claim: If an equilateral polygon is inscribed in a circle, then it is a regular polygon.

 

GSP Sketch and Proof

 

 

Claim:

Connecting the midpoints of the sides of a triangle divides the triangle into four little triangles. Show that the little triangles are similar to the original triangle and that all four of these little triangles are congruent.

 

GSP Sketch and Proof