SOLUTION: What is the converse,inverse and contrapositive of this theorem? The diagonals of a parallelogram bisect each other.

Original statement:
The diagonals of a parallelogram bisect each other.

First re-write the original sentence using the words "if" and "then":

The original statement is talking about two line segments, so

Let p stand for "two line segments are diagonals of a parallelogram"

Let q stand for "two line segments bisect each other".

ORIGINAL STATEMENT REWRITTEN IN "IF-THEN" FORM:  p -> q
If two line segments are diagonals of a parallelogram, then the two line
segments bisect each other.

The clause between the "if" and the "then" is called the "antecedent".
The clause following the "then" is called the "consequence".

In the above the clause p, or "two line segments are diagonals of a
parallelogram" is the antecedent.

In the above the clause q, or "two line segments bisect each other" is the
consequence.

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THE CONVERSE: The converse swaps the antecedent and the consequence of the
original statement:

q -> p

If two line segments bisect each other, then the two line segments are
diagonals of a parallelogram.

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THE INVERSE:  The inverse keeps antecedent and the consequence of the original
statement but negates each:

~p -> ~q
  
If two line segments are NOT diagonals of a parallelogram, then the two line
segments DO NOT bisect each other.

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THE CONTRAPOSITIVE:  The Contrapositive does both of the above.  It swaps the
antecedent and the consequence of the original statement and also negates them
both.

~q -> ~p

If two line segments DO NOT bisect each other, then the two line segments are
NOT diagonals of a parallelogram.

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The original statement and the contrapositive are equivalent, that is,
if one is true, so is the other, and if one is false, so is the other.

The inverse and the converse are also equivalent.

But the equivalent original statement and the contrapositive
are not necessarily equivalent to the converse and the inverse. 

Edwin