2-2+Biconditional+Statements

this section will show you that all definitions can be interpreted "forwards" and "backwards" and can be either true or false. Statements like this are usually given in //if and only-if// form as biconditional statements, or as a conditional statement given in //only-if// and //if-then// forms where the hypothesis is followed by the conclusion. A conditional statement can be written as a converse statement which is the reverse of the conditional statement, and is written where the conclusion is the hypothesis and the hypothesis becomes the conclusion.


 * vocabulary:**
 * perpendicular lines**- lines that intersect to form a right angle
 * line perpendicular to a plane**- a line that intersects a plane at a right angle and is perpendicular to every line in the plane
 * biconditional statement**- a statement written as a conditional and converse using the phrase if and only if (iff); it is also the same as writing a conditional statement and its converse.


 * examples:**

1. based on the diagram is AC perpendicular to DB?


 * solution:** Yes, because the right angle symbol in the diagram shows that line AC intersects line DB to for a right angle, so the lines are perpendicular.

2. conditional statements are not always written in //if-then// form, and are sometimes written in //only-if// form.

It is Thursday, **only if** I have swim practice. ↑ Hypothesis ↑ Conclusion

statement rewritten in if-then form: **If** it is Thursday, **then** I have swim practice.

statement written as a converse (or reverse): If i have swim practice, then it is Thursday.

statement written as a biconditional statement: It is Thursday, **if and only if** i have swim practice.

3. conditional: **If** B lies between points G and E, **then** GB+EB=GE

converse: **If** GB+EB=GE, **then** B lies between points G and E

combining these two statements results in a true biconditional statemet.

biconditional: Point B lies between points G and E **if and only if** GB+EB=GE




 * practice problems:**

1. Is line L2 perpendicular to line L1?



2. write the conditional statement as a biconditional statement.

If it is raining, then I need an umbrella.

3. Write the following conditional statement as its converse and biconditional.

If i am eating cookies, then I want a glass of milk.

4. Write and conditional and converse statement for the following biconditional statement.

A points on a line is collinear if and only if they are on the same line.

biconditional [|logic- biconditional statements]
 * web pages for extra help**:


 * pages in textbook:** 79-87