Converse, Inverse, Contrapositive Given an if-then statement "if p , then q ," we can create three related statements: A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause.
The converse in geometry applies to a conditional statement. 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. This is often used in theorems and problems involving proofs in geometry.
The definition of converse in math, or more specifically logical reasoning, is the switching of the hypothesis and conclusion of a conditional statement. An example is if it is raining then there ...
Converse. Switching the hypothesis and conclusion of a conditional statement. For example, the converse of "If it is raining then the grass is wet" is "If the grass is wet then it is raining." Note: As in the example, a proposition may be true but have a false converse.
I should note that this 'converse of a statement' is useful in geometry, not just when discussing my dietary choices. Let's first talk about the two parts of a conditional statement.
So the converse of this statement is not true as well but not every statement in geometry whose converse is going to be false. So that's not always going to happen. I just gave two examples here where if you take the if and the then statement, switch them and evaluate them, you can find counter examples which makes the converse not true.
A converse in geometry is when you take an conditional statement and reverse the premise “if p” and the conclusion “then q”. Given a polygon, if it is a square then it has 4 sides. This statement is true. Now reverse the statements, Given a polygo...
Menu Geometry / Proof / If-then statement. When we previously discussed inductive reasoning we based our reasoning on examples and on data from earlier events. If we instead use facts, rules and definitions then it's called deductive reasoning. ... If we exchange the position of the hypothesis and the conclusion we get a converse statement: ...
Contrapositive. Switching the hypothesis and conclusion of a conditional statement and negating both. For example, the contrapositive of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining."
While we've seen that it's possible for a statement to be true while its converse is false, it turns out that the contrapositive is better behaved. Whenever a conditional statement is true, its contrapositive is also true and vice versa. Similarly, a statement's converse and its inverse are always either both true or both false.