STANDARD G.CO.C.11
GEO

Prove and apply theorems about parallelograms.
• Include multi-step proofs and algebraic problems built upon these concepts.
• The inclusive definition of a trapezoid will be utilized, which defines a trapezoid as “A quadrilateral with at least one pair of parallel sides.”
• Examples of theorems include but are not limited to:
   o A diagonal divides a parallelogram into two congruent triangles.
   o Opposite sides/angles of a parallelogram are congruent.
   o The diagonals of parallelogram bisect each other.
   o If the diagonals of quadrilateral bisect each other, then quadrilateral is a parallelogram.
   o If the diagonals of a parallelogram are congruent then the parallelogram is a rectangle.
• Additional theorems covered allow for proving that a given quadrilateral is a particular parallelogram (rhombus, rectangle, square) based on given properties.