CK12 - Geometry

contrapositive,then you can do this sincethe statementand its contrapositiveare equivalent.

Example 1

If then. True.

Statement:

If , then. False.

Converse:

A counterexampleis

, where but is not

Inverse: If is not then is not. False.

A counterexampleis

where is not but =

Contrapositive: If is not , then is not. True.

If is not , then and is not

Example 2

If then is the midpointof. False(as shownbelow).

Statement:

Needs

Converse: If is the midpointof , then. True.

If , then is not the midpointof. True.

Inverse:

If is not the midpointof , then False(see the diagramabove).

Contrapositive:

BiconditionalStatements

You recallthat the converseof “If then ” is “If then .” Whenthesetwo are combined,we havea
biconditionalstatement.

Biconditional: and

In symbols,this is writtenas: