What is the converse of the statement “If a triangles is isosceles, then it has two congruent sides”

Question

kinggeorge · Answer

If a triangle has two congruent sides it is isosceles.

anonymous · Answer

THANK YOU

kinggeorge · Answer

You're welcome.

anonymous · Answer

If p: two lines intersect and q: they share a common point, write ~p--->~q as a conditional statement

kinggeorge · Answer

First, can you tell me what ~p is in words?

anonymous · Answer

i have no idea . that just what it shows on my homework and i dont have a book because i do online school

kinggeorge · Answer

To get ~p in words, tell me the opposite of this statement "Two lines intersect"

anonymous · Answer

? can you re word that

kinggeorge · Answer

What's the opposite of "Two lines intersect"?

anonymous · Answer

Parallel lines?

kinggeorge · Answer

Basically. For this problem, you would say "Two lines don't intersect"

Now what about ~q. What's the opposite of "They share a common point?"

anonymous · Answer

then they dont share a common point?

kinggeorge · Answer

Precisely. Now we need to turn it into a conditional statement.

kinggeorge · Answer

$\neg \;p \Rightarrow \neg \;q$ is equivalent to the statement

If not p, then not q.

Since we know not p and not q, we can just combine the statements into "If two lines don't intersect, then they don't share a common point."