Question

What is the converse of a statement that uses the form q if p? Since the conclusion is already first?
Ex: Two segments are congruent if they have the same length.
Would the converse still be: If two segments are congruent, then they have the same length?

Forms of conditional statements:
If p, then q.
p implies q.
p of if q.
q if p.

Answer 1

If p then q means that q is true if p is true.

I will bring an umbrella if it rains
is the same as
If it rains I will bring an umbrella

Conversely, would this be true?

If I bring an umbrella then it will rain

The answer is obviously NO

So the converse is not always true

However, if you know the converse is true, via proof/definition, then you can say

p if q, which is the converse

In your example about congruence, the converse statement would be valid because both q if p and p if q are true.

Answer 2

To write converses, the conclusion is always first regardless of the order of it in the conditional statement right?

Answer 3

Because converses are "if conclusion, then hypotenuse."

Answer 4

hypothesis* i mean, not hypotenuse

Answer 5

im pretty sure that converses and the original statement SOMETIMES contradict, so be aware

Answer 6

I'm just confused on how to write converses if the original statement's form is "q if p". I'm not concerned if the converse is true or false... Because in most conditional statements, the form is "if p, then q" and all you do for the converse is switch the order.

But in a converse, the conclusion is always written first right?

Answer 7

No, it can be written two ways

p if q is the converse of q if p
But p if q can also be written as if q then p and so in this case q came first. The most important is what follow the if statement and what is implied by it

For example

The converse of if it rains (p) then I will use an umbrella (q) can be written as p if q or if q then p or if I use and umbrella (q) then it will rain (p).

Answer 8

Oh, that makes more sense. Thank you very much for answering!

Answer 9

You're welcome!