Conditional Statements

A conditional statement is a statement of the form "If A, then B." The part following the if is called the hypothesis. The part following the then is called the conclusion. For example: If you are a monkey, then you like bananas. The hypothesis in this conditional is in blue and the conclusion in orange. Conditional statements also have other things related to them called the converse, the inverse, and the contrapositive. Another term to be familiar with is negation or negate, which means the denial of a statement. If a statement is true, the negation would be false. Converse means (in geometric terms) the exchange of the hypothesis with the conclusion. With our statement above, the converse would be If you like bananas, then you are a monkey. The inverse is negating the hypothesis and the conclusion. If you are not a monkey, then you do not like bananas. The contrapositive is the most confusing form. It is the negation of the converse. This means that to get the contrapositive you must first find the converse of the statement and then negate it.

Statement: If a shape is a quadrilateral, then it is a polygon. This is true.

Converse: If a shape is a polygon, then it is a quadrilateral. This is false. Triangles, pentagons, and octagons are polygons, but have more than four sides.

Inverse: If a shape is not a quadrilateral, then it is not a polygon. This is false. Triangles, pentagons, and octagons are polygons, but are not quadrilaterals.

Contrapositive: If a shape is not a polygon, then it is not a quadrilateral. This is true

Statement: If a triangle is equilateral, then it is equiangular. This is true.

Converse: If a triangle is equiangular, then it is equilateral. This is true

Inverse: If a triangle is not equilateral, then it is not equiangular. This is true.

Contrapositive: If a triangle is not equiangular, then it is not equilateral. This is also true.

Statement: If a quadrilateral has four congruent sides, then it is a rhombus. This is true.

Converse: If a quadrilateral is a rhombus, then it has four congruent sides.

Inverse: If a quadrilateral does not have four congruent sides, then it is not a rhombus. This statement is true.

Contrapositive: If a quadrilateral does not have four of congruent sides, then it is not a rhombus. This statement is true.

Statement: If a triangle has four sides, then it is a gastropod. This is not true.

Converse: If a triangle is a gastropod, then it has four sides. This is not true.

Inverse: If a triangle does not have four sides, then it is not a gastropod. This is true.

Contrapositive: If a triangle is not a gastropod, then it does not have four sides. This is true.

Statement: If a quadrilateral has four right angles, then it is a rectangle.

Converse: If a quadrilateral is a rectangle, then it has four right angles.

Inverse: If a quadrilateral does not have four right angles, then it is not a rectangle.

Contrapositive: If a quadrilateral is not a rectangle, then it does not have four right angles.