Proofs

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easilyconfuzzeled

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OK so math is my worst subject and i am really confused. I'm doing proofs in my geometry class and this is the question that I'm stuck on.
If 3 - 2x = 13, then x = -5 and its telling me to write the converse of this statement.
I have no idea what I'm doing. :? HELP!

~easilyconfuzzeled~
 
\(\displaystyle The\ converse\ is......\ if\ x=-5,\ then\ 3-2x=13.\)

\(\displaystyle Is\ that\ converse\ statement\ also\ true?\)
 
\(\displaystyle The\ converse\ means......\)

\(\displaystyle If\ you\ say\ it\ backwards,\ is\ it\ still\ true?\)
\(\displaystyle Example.....\)
\(\displaystyle A\ square\ shape\ is\ a\ rectangle\)
\(\displaystyle The\ converse\ statement....\ A\ rectangle\ is\ a\ square\ shape...\ is\ untrue\ in\ general.\)

\(\displaystyle In\ your\ case\ just\ put\ x=-5\ into\ 3-2x\ and\ check\ you\ still\ get\ 13.\)
\(\displaystyle It\ still\ means\ the\ same\ thing.\)
 
So would the converse of this statement, If two angles are both obtuse, the two angles are equal, be, If two angles are equal then they are obtuse?
 
easilyconfuzzeled said:
So would the converse of this statement, If two angles are both obtuse, the two angles are equal, be, If two angles are equal then they are obtuse?
Click to expand...

Yes...that is the converse of the original statement.

Now...you might want to look at whether the original statement, "If two angles are both obtuse, then the two angles are equal" is true. Suppose you have two angles which are both obtuse....suppose m<A = 100 and m<B = 150. Would you agree that both <A and <B are obtuse? Are the two angles equal?

Then look at the converse, "If two angles are equal, then they are obtuse." Is that true? Suppose m<A = 45 and m<B = 45. Surely <A = <B. But are <A and <B both obtuse?

In this case, the original statement and its converse are both false.

Look at this statement: If two angles are right angles, then the two angles are supplementary.

Is that statement true?

The converse is "If two angles are supplementary, then the two angles are right angles." Is the converse true?

When one is dealing with the converse of a statement, the "truth value" of the original statement does not tell you anything about the "truth value" of the converse. A true statement may have a true converse, or it may have a false converse. A false statement may have a false converse, or it may have a true converse. Knowing the truth value of the original statement does not (IN GENERAL) tell you anything about the truth value of the converse of that statement.
 
OK I am stuck on another one. It says...
If two angle's are supplementary, then they are not equal.
Would the converse be...
If two angle's are not equal, then they are supplementary?
 
\(\displaystyle Exactly!\)
\(\displaystyle You're\ definately\ getting\ the\ hang\ of\ it.\)
\(\displaystyle Of\ course,\ the\ original\ angles\ must\ not\ be\ right-angles\ for\ the\ statement\ to\ be\ true.\)
 
\(\displaystyle Also,\ it\ will\ be\ extremely\ rare\ for\ unequal\ angles\ to\ be\ supplementary,\\)
\(\displaystyle won't\ they?\)
 
\(\displaystyle It\ would\ be\ ok\ if\ the\ angles\ had\ to\ add\ up\ to\ 180\ degrees.\)
\(\displaystyle Pick\ any\ 2\ unequal\ angles\ and\ there\ is\ little\ chance\ of\ them\ summing\ to\ 180\ degrees,\ in\ general.\)
 
i have a math question!!!! for proofs the question is: when 2 lines intersect, the measures of vertical angels are equal.
 
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