If a quadrilateral is a square, then it is a rectangle.
True âś“
Converse
If a quadrilateral is a rectangle, then it is a square.
False *
Inverse
If a quadrilateral is not a square, then it is not a rectangle.
False *
Contrapositive
If a quadrilateral is not a rectangle, then it is not a square.
True âś“
For explanation see solution.
Practice makes perfect
Let's begin with recalling that a square is a rectangle with four sides that are congruent. Now we will take a look at the given statement.
If a quadrilateral is a square,
then it is a rectangle.
As we recalled, a square is a special case of rectangle that has all congruent sides. This means that each square is a rectangle at the same time. Therefore, this statement is true.
Converse Statement
To create a converse statement, we should exchange a square and a rectangle.
Original Statement
Converse Statement
If a quadrilateral is a square, then it is a rectangle.
If a quadrilateral is a rectangle, then it is a square.
Since not all rectangles have congruent sides, the converse statement is false.
Inverse Statement
Next, to create an inverse statement we should add not to each part of the statement.
Original Statement
Inverse Statement
If a quadrilateral is a square, then it is a rectangle.
If a quadrilateral is not a square, then it is not a rectangle.
Let's notice that a quadrilateral with two pairs of congruent sides and all right angles is rectangle, but it is not necessarily a square, which has all four congruent sides. Therefore, the inverse statement is false.
Contrapositive Statement
Finally we will create a contrapositive statement. To do this, we should exchange a square and a rectangle, and we should add not to each part of the statement.
Original Statement
Contrapositive Statement
If a quadrilateral is a square, then it is a rectangle.
If a quadrilateral is not a rectangle, then it is not a square.
A quadrilateral needs to satisfy all conditions of rectangles to be a square. Therefore, if it is not a rectangle, it cannot be a square. This means that this statement is true.
