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What are the converse, invere and contrapositive in geometry?

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Quick Answer

In geometry, converse, inverse and contrapositive are conditional statements consisting of a hypothesis and a conclusion. These statements are also known as “if-then statements.” The hypothesis part of a conditional statement is the “if," and the “then” part is the conclusion. The conclusion is the result of a hypothesis.

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A conditional statement is represented in geometry by the symbols "if p, then q." The p represents the hypothesis and the q represents the conclusion.

Example: “If it is sunny, then I will wash my car.”

The converse of a conditional statement occurs when the hypothesis and the conclusion switch places. Instead of "if p, then q," the converse is "if q, then p."

Example: “If I wash my car, then it is sunny.”

The inverse of a conditional statement is when both the hypothesis and the conclusion are negated. The symbols of a negated hypothesis and conclusion are ~p and ~q meaning "if not p, then not q."

Example: “If it is not sunny, then I will not wash my car.”

The contrapositive of a conditional statement is when both the hypothesis and conclusion have switched places and have been negated. In other words, it is a negated converse statement, "if not q, then not p."

Example: “If I do not wash my car, then it is not sunny.”

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