paraguy
def
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
Using the definition, all of the parallelogram properties, when stated as theorems, can be "proven" true.

The properties (theorems) will be stated in "if ...then" form. Both the theorem and its converse (where you swap the "if" and "then" expressions) will be examined.

Click PROOFsmall in the charts below to see each proof.
The * means proof is directly referenced in Common Core.
While one method of proof will be shown, other methods are also possible.
Use the following, when GIVEN a parallelogram:
sides
DEFINITION: A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
para1
THEOREM: If a quadrilateral is a parallelogram, it has 2 sets of opposite sides congruent. 
PROOFsmall*
para2
angles
THEOREM: If a quadrilateral is a parallelogram, it has 2 sets of opposite angles congruent. 
PROOFsmall*
para3
THEOREM: If a quadrilateral is a parallelogram, it has consecutive angles which are supplementary.
PROOFsmall
para4
disgonals
THEOREM: If a quadrilateral is a parallelogram, it has diagonals which bisect each other. 
PROOFsmall*
para5
THEOREM: If a quadrilateral is a parallelogram, it has diagonals which form 2 congruent triangles. 
PROOFsmall
para6



Use the following, to PROVE a parallelogram:
sides
DEFINITION: A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
para1
THEOREM: If a quadrilateral has 2 sets of opposite sides congruent, then it is a parallelogram. 
PROOFsmall*
para2
angles
THEOREM: If a quadrilateral has 2 sets of opposite angles congruent, then it is a parallelogram. 
PROOFsmall*
para3
THEOREM: If a quadrilateral has consecutive angles which are supplementary, then it is a parallelogram. 
PROOFsmall
para4
diag
THEOREM: If a quadrilateral has diagonals which bisect each other, then it is a parallelogram. 
PROOFsmall*
para5
combo
THEOREM: If a quadrilateral has one set of opposite sides which are both congruent and parallel, then it is a parallelogram.
PROOFsmall
This last method can save time and energy when working a proof!
para7

 


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