The converse of the Pythagorean Theorem helps you to find out if a triangle is a right triangle. Do you know what converse means? The converse of a theorem is a theorem if and only if and are equivalent, i.e., . Truth tables get a little more complicated when conjunctions and disjunctions of statements are included. This is often used in theorems and problems involving proofs in geometry. Statement: If x = 3 then x^2 = 9 Similarly, if two alternate interior or alternate exterior angles are congruent, the lines are parallel . In this non-linear system, users are free to take whatever path through the material best serves their needs. The converse of the theorem is true as well. Sometimes, it may be necessary to evaluate the truth value of a conditional statement and of its converse. So if a statement is true then you know that the contrapositive statement is also true. Given the statement "if , then ," or , the converse is "if , then ." Converse : If one angle of a triangle measures 90 degrees, then the triangle is a right triangle. The converse of a theorem happens when … For example, the converse of "If a thing is a dog then it is a mammal" is "If a thing is a mammal then it is a dog." ... by definition, always have opposite truth values. Well if you look closely youâ ll see that the original statement has the same truths as the contrapositive. Let's look at one more and apply it to geometry. Basically, the converse of the Pythagorean Theorem states that whenever the sum of the squares of two sides equal to the square of the third side of the triangle, the triangle is a right triangle. What Does Converse Mean? Also the converse has the same truth table as the inverse. Geometry: Logic Statements quizzes about important details and events in every section of the book. If an angle measures 88 degrees, then it is acute. I agree it seems to say nothing. In a conditional statement, the words "if" and "then" are used to show assumptions and conclusions that are to be arrived at using logical reasoning. The converse in geometry applies to a conditional statement. In math, when you have a theorem, you likely have a converse theorem. The converse is not true. So let's find our converse. If two corresponding angles are congruent, then the two lines cut by the transversal must be parallel. It means switch what was after "if" with what was after "then." Illustrated definition of Converse (logic): A conditional statement (if ... then ...) made by swapping the if and then parts of another statement. Same goes for converse and inverse statements. Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. These unique features make Virtual Nerd a viable alternative to private tutoring. Converse. This is shown in the truth table. $\begingroup$ @PatrickDaSilva: The first line is given as the second of the eight postulates in [Birkhoff and MacLane, Surveys of Modern Algebra] for the definition of a commutative ring. geometry: the converse of the conditional statment. That's true by definition an acute angle is any angle that measures less than 90 degrees but more than 0 degrees.