They could both be false and you could still write a true biconditional statement ('My pet goat draws polygons if and only if my pet goat buys art supplies online.'). You can do this if and only if both conditional and converse statements have the same truth value. My polygon has only three sides if and only if I have a triangle. I have a triangle if and only if my polygon has only three sides. Since both statements are true, we can write two biconditional statements: (true)Ĭonverse: If my polygon has only three sides, then I have a triangle. Let's apply the same concept of switching conclusion and hypothesis to one of the conditional geometry statements:Ĭonditional: If I have a triangle, then my polygon has only three sides.Ĭonverse: If my polygon has only three sides, then I have a triangle.īoth the conditional and converse statements must be true to produce a biconditional statement.Ĭonditional: If I have a triangle, then my polygon has only three sides. Your homework being eaten does not automatically mean you have a goat. This converse statement is not true, as you can conceive of something … or someone … else eating your homework: your dog, your little brother. Take the first conditional statement from above:Ĭonclusion: … then my homework will be eaten.Ĭonverse: If my homework is eaten, then I have a pet goat. You may 'clean up' the two parts for grammar without affecting the logic. To create a converse statement for a given conditional statement, switch the hypothesis and the conclusion. Whether the conditional statement is true or false does not matter (well, it will eventually), so long as the second part (the conclusion) relates to, and is dependent on, the first part (the hypothesis).

If the quadrilateral has four congruent sides and angles, then the quadrilateral is a square.Įach of these conditional statements has a hypothesis ('If …') and a conclusion (' …, then …'). If I ask more questions in class, then I will understand the mathematics better. If I eat lunch, then my mood will improve. If the polygon has only four sides, then the polygon is a quadrilateral. If I have a triangle, then my polygon has only three sides. If I have a pet goat, then my homework will be eaten. In logic, concepts can be conditional, using an if-then statement: Then we will see how these logic tools apply to geometry. To understand biconditional statements, we first need to review conditional and converse statements. One example is a biconditional statement. Geometry and logic cross paths many ways.

If we remove the if-then part of a true conditional statement, combine the hypothesis and conclusion, and tuck in a phrase 'if and only if,' we can create biconditional statements. Both the conditional and converse statements must be true to produce a biconditional statement. A biconditional statement combines a conditional statement with its converse statement.

Converse geometry problems