Question

the following statement is given: \if a rigid transformation has been performed, then angle measure and distance are preserved.\ select the boxes to identify what could be the converse, inverse, and contrapositive of the given statement. if a rigid transformation has not been performed, then angle measure and distance are not preserved. if angle measure and distance are preserved, then a rigid transformation has been performed. if angle measure and distance are not preserved, then a rigid transformation has not been performed.

Explanation:

Step1: Recall definitions

Let \(p\): "a rigid transformation has been performed" and \(q\): "angle measure and distance are preserved". The original statement is \(p
ightarrow q\).

• The converse is \(q

ightarrow p\).

• The inverse is \(

eg p
ightarrow
eg q\).

• The contrapositive is \(

eg q
ightarrow
eg p\).

Step2: Analyze each statement

• For "If a rigid transformation has not been performed, then angle measure and distance are not preserved" (\(

eg p
ightarrow
eg q\)), this is the inverse.

• For "If angle measure and distance are preserved, then a rigid transformation has been performed" (\(q

ightarrow p\)), this is the converse.

• For "If angle measure and distance are not preserved, then a rigid transformation has not been performed" (\(

eg q
ightarrow
eg p\)), this is the contrapositive.

Answer:

Contrapositive	Inverse	Converse