question 1-1
a true statement is given
\if three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.\
select the statement that represents the converse of this statement
if three sides of one triangle are congruent to three sides of a second triangle if and only if the triangles are congruent.
three sides of one triangle are congruent to three sides of a second triangle, then the triangles are not congruent.
if two triangles are not congruent to three sides of a second triangle, then the triangles are not congruent.
if three sides of one triangle are not congruent to three sides of a second triangle, then three sides of the one triangle are congruent to three sides of the second triangle.
if one triangle is congruent to a second triangle, then three sides of the one triangle are congruent to three sides of the second triangle.
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# Brief Explanations:
The original statement is "If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent." The converse of a conditional statement "If $ p $, then $ q $" is "If $ q $, then $ p $". Here, $ p $ is "three sides of one triangle are congruent to three sides of a second triangle" and $ q $ is "the triangles are congruent". So the converse should be "If the triangles are congruent, then three sides of one triangle are congruent to three sides of the second triangle", which matches the option "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent" (wait, no, re - examining: the correct converse is "If the triangles are congruent, then three sides of one triangle are congruent to three sides of the second triangle" which is the option "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent"? Wait, no, let's re - express. The original is $ p
ightarrow q $, converse is $ q
ightarrow p $. So $ q $ is "triangles are congruent", $ p $ is "three sides of one triangle are congruent to three sides of a second triangle". So converse is "If the triangles are congruent, then three sides of one triangle are congruent to three sides of the second triangle" which is the option "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent"? Wait, no, the option "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent" is the original statement? Wait, no, the first option is "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent" – no, wait the original statement is "If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent". The converse would be "If the triangles are congruent, then three sides of one triangle are congruent to three sides of the second triangle", which is the option "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent"? Wait, no, the option "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent" is the same as the original? No, maybe I misread. Wait the options:

1. Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent – this is the original statement? No, the original statement is "If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent". Wait, no, the first option is "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent" – maybe the wording is a bit off, but the converse of $ p
ightarrow q $ is $ q
ightarrow p $. So $ p $: three sides of one triangle are congruent to three sides of a second triangle; $ q $: the triangles are congruent. So converse is $ q
ightarrow p $, i.e., "If the triangles are congruent, then three sides of one triangle are congruent to three sides of the second triangle", which is the option "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent"? Wait, no, the option "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent" is $ p
ightarrow q $, but maybe the option is written as "If the triangles are congruent, then three sides of one triangle are congruent to three sides of the second triangle" which is the same as "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent" – no, that's not. Wait, maybe the correct option is the one that has $ q
ightarrow p $, so "If the triangles are congruent, then three sides of one triangle are congruent to three sides of the second triangle" which is the option "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent"? No, I think I made a mistake. Let's re - state:

Original statement: $ p $: three sides of one triangle ≅ three sides of a second triangle; $ q $: triangles are congruent. So $ p
ightarrow q $.

Converse: $ q
ightarrow p $, i.e., "If the triangles are congruent, then three sides of one triangle are congruent to three sides of the second triangle", which is the option "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent" – no, that's $ p
ightarrow q $. Wait, maybe the option is written as "If the triangles are congruent, then three sides of one triangle are congruent to three sides of the second triangle" which is the same as the option "Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent" – no, that's not. Wait, looking at the options again:

Option 1: Three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.

Option 2: If two triangles are not congruent, then three sides of one triangle are not congruent to three sides of a second triangle. (This is the contrapositive)

Option 3: If three sides of one triangle are not congruent to three sides of a second triangle, then the triangles are not congruent. (This is the inverse)

Option 4: If one triangle is congruent to a second triangle, then three sides of the one triangle are congruent to three sides of the second triangle. (This is $ q
ightarrow p $, the converse)

Ah! So option 4 is the converse. So the correct option is "If one triangle is congruent to a second triangle, then three sides of the one triangle are congruent to three sides of the second triangle".

# Answer:
If one triangle is congruent to a second triangle, then three sides of the one triangle are congruent to three sides of the second triangle (the fourth option in the list of choices).

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