Question

question 1 - 5
complete the table to show which statement is the converse, inverse, or contrapositive of the conditional statement shown.
conditional statement: if two triangles are congruent, then they have the same side lengths.
if two triangles are not congruent, then they do not have the same side lengths.
if two triangles have the same side lengths, then they are congruent.
if two triangles do not have the same side lengths, then they are not congruent.
converse
inverse
contrapositive

Explanation:

• Converse: The converse of a conditional statement "If \(p\), then \(q\)" is "If \(q\), then \(p\)". The conditional statement is "If two triangles are congruent, then they have the same side lengths". So the converse is "If two triangles have the same side lengths, then they are congruent".
• Inverse: The inverse of "If \(p\), then \(q\)" is "If not \(p\), then not \(q\)". For the given conditional, the inverse is "If two triangles are not congruent, then they do not have the same side lengths".
• Contrapositive: The contrapositive of "If \(p\), then \(q\)" is "If not \(q\), then not \(p\)". Here, it is "If two triangles do not have the same side lengths, then they are not congruent".

Answer:

• Converse: If two triangles have the same side lengths, then they are congruent.
• Inverse: If two triangles are not congruent, then they do not have the same side lengths.
• Contrapositive: If two triangles do not have the same side lengths, then they are not congruent.