CK12 - Geometry

Hereare two true statements.

If and are a linearpair, then.

and are a linearpair.

Whatconclusiondo we drawfrom thesetwo statements?

The next exampleis a warningnot to turn the law of detachmentaround.

Example 5

Hereare two true statements.

If and are a linearpair, then

and

Whatconclusioncan we drawfrom thesetwo statements?

None!Thesestatementsare in the form

Notethat since and , we also knowthat , but this
doesnot meanthat they are a linearpair.

The law of detachmentdoesnot apply. No furtherconclusionis justified.

You mightbe temptedto concludethat and are a linearpair, but if you thinkaboutit you will re-

alize that wouldnot be justified.For example,in the rectanglebelow and (and

, but , and are definitelyNOTa linearpair.

Now let’s look ahead.We will be doingsomemorecomplexdeductivereasoningas we moveaheadin ge-
ometry. In manycaseswe will buildchainsof connectedif-thenstatements,leadingto a desiredconclusion.
Startwith a simplifiedexample.

Example 6

Supposethe followingstatementsare true.

1. If Pete is late, Markwill be late.