CK12 - Geometry

We read as: “ if and only if ”

Example 3

True statement: if and only if is an obtuseangle.

You can breakthis downto say:

If then is an obtuse angle and if is an obtuse angle then

.

Noticethat both partsof this biconditionalare true; the biconditionalitself is true.

You mostlikelyrecognizethis as thedefinitionof an obtuseangle.

Geometricdefinitionsare biconditionalstatementsthat are true.

Example 4

Let be

Let be

a.Is true?

Yes.

is if then

Fromalgebrawe knowthat if then and If , then we knowthat

So if then , or is true.

b.Is true?

No.

is if , then

Fromalgebrawe knowthat if , then

However, doesnot guaranteethat

can be less that but still not less than , for exampleif is.

So if , then , or , is false.

c.Is true?

No.

is if and only if