Relationship between the diagonals of a Parallelogram - Proof
For my Proof for a Geometric Theorem, i chose to prove that a rectangles diagonals are congruent. The given is that Parallelogram ABCE is a rectangle. AB and CE are congruent, because of the properties of a rectangle. Using the rule that opposite sides of a parallelogram are congruent, we know that CE and BA are congruent as well. Angle A, B, C, and E are all 90 degrees because a rectangle has 4 right angles. Using the SAS, Triangle BAE is the same as Triangle CEA. Finally, Segment AC is the same as angle BE because of corresponding parts of congruent triangles, which proves that diagonals are congruent in a rectangle.