In the converse of a statement we switch the hypothesis with the conclusion.
Converse of the Statement: If ABCD is a parallelogram, then ABCD is a square. Are They True? The statement is true and its converse is false.
Practice makes perfect
We want to write the converse of the given statement. In this statement we have a hypothesis and a conclusion. A hypothesis tells us about the condition. When this condition is satisfied, the conclusion is true.
Statement
If {\color{#0000FF}{\underbrace{ABCD\text{ is a square}}_\text{hypothesis}}}, then ABCDis a parallelogram_(conclusion).
Now, in the converse of the statement we switch the hypothesis with the conclusion. This means that the previous hypothesis becomes the new conclusion and the previous conclusion becomes the new hypothesis.
Converse of the Statement
If ABCDis a parallelogram_(new hypothesis), then {\color{#0000FF}{\underbrace{ABCD\text{ is a square}}_\text{new conclusion}}}.
Let's think if our statement and its converse are true or false. To do so, let's recall that a parallelogram has two pairs of parallel sides.
We can see that each square is a quadrilateral because it has two pairs of parallel sides. However, not every parallelogram is a square because a parallelogram does not have to have right angles or congruent sides. This means that our statement is true but the converse of the statement is false.
