Question

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.
○ three sides of one triangle are congruent to three sides of a second triangle if and only if the triangles are congruent.
○ if two triangles are not congruent, then three sides of one triangle are not congruent to three sides of the other triangle.
○ if three sides of one triangle are not congruent to three sides of a second triangle, then the triangles are not congruent.
○ if one triangle is congruent to a second triangle, then three sides of the one triangle are congruent to three sides of the second triangl

Explanation:

To find the converse of a conditional statement "If \( p \), then \( q \)", we swap the hypothesis (\( p \)) and the conclusion (\( q \)). The original statement is "If three sides of one triangle are congruent to three sides of a second triangle (\( p \)), then the triangles are congruent (\( q \))". So the converse should be "If the triangles are congruent (\( q \)), then three sides of one triangle are congruent to three sides of the second triangle (\( p \))". We check each option:

• First option: Is a biconditional (if and only if), not a converse.
• Second option: Is the contrapositive of the inverse, not the converse.
• Third option: Is the inverse, not the converse.
• Fourth option: Is the contrapositive, not the converse.
• Fifth option: Swaps \( p \) and \( q \), so it is the converse.

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