To prove a statement true, the converse must also be proven true, while to disprove the statement, it is necessary to prove the converse false. You Can Read: Are Cole Haan Oulet Shoes Different? How is Converse used in Geometry?Īnswer: Converse is commonly used in geometry to prove or disprove a theorem or statement. This process is used to prove or disprove a theorem, by showing that if a statement’s converse is false, then the original statement must also be false. Specifically, it involves making the hypothesis the conclusion and vice versa. For example, if the statement is “If A, then B,” the converse is logically equivalent to the original statement, but the contrapositive is logically equivalent to the statement “If not A, then not B.” Few Frequently Asked Questions What is Converse in Geometry?Īnswer: Converse in geometry is the process of switching two statements around to form a new statement. The converse of a statement is logically equivalent to the original statement, whereas the contrapositive is logically equivalent to the inverse of the original statement. Then, one can use the contrapositive to prove that if the corresponding angles are equal, then the lines must be parallel. For example, if one wants to prove that two lines are parallel, one might start by proving the converse statement that if the lines are not parallel, then their corresponding angles are not equal. The converse is usually used as a starting point to prove a theorem, while the contrapositive is usually used to prove the converse. The converse and the contrapositive can both be used to prove theorems, but they are used in different ways. The contrapositive, however, states “If not B, then not A,” which implies that A and B are related in some way. For example, if the statement is “If A, then B,” the converse is “If B, then A,” but this does not necessarily mean that A and B are related. The converse of a statement does not necessarily mean the same thing as the original statement, whereas the contrapositive does. For example, if a statement is “If A, then B,” the converse would be “If B, then A,” and the contrapositive would be “If not B, then not A.” Difference in Meaning The converse of a statement is the statement with the terms reversed, while the contrapositive is the statement with the terms both reversed and negated. What is the Difference Between Converse and Contrapositive? From there, one can use the true statement to solve the problem. By identifying the statement and its converse, one can identify which statement is true and which is false. This is because the converse of a statement is equivalent to the statement itself, so if the converse is proven to be true, then the statement must also be true.Ĭonverse can also be used to solve geometry problems. By proving the converse of a statement, one can prove that the statement is true.
The converse of a statement can be used to prove theorems in geometry. You Can Read: Are Timberland Boots True To Size Uk? Uses of Converse in Geometry
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