Question

question 1-2
a true statement is given.
\if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.\
select the statement that represents the inverse of this statement.

• if two triangles are not congruent, then two sides and the included angle of one triangle are not congruent to two sides and the included angle of the other triangle
• two triangles are congruent if and only if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle
• if two triangles are congruent, then two sides and the included angle of one of the triangles are congruent to two sides and the included angle of the second triangle
• if two sides and the included angle of one triangle are not congruent to two sides and the included angle of a second triangle, then the triangles are not congruent

Explanation:

To find the inverse of a conditional statement "If \( p \), then \( q \)", we use the form "If not \( q \), then not \( p \)". The original statement is: "If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent." Here, \( p \) is "two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle" and \( q \) is "the triangles are congruent". The inverse should be "If the triangles are not congruent (\(
eg q \)), then two sides and the included angle of one triangle are not congruent to two sides and the included angle of a second triangle (\(
eg p \))". Looking at the options, the first option ("If two triangles are not congruent, then two sides and the included angle of one triangle are not congruent to two sides and the included angle of the other triangle") matches this inverse form.

Answer:

A. If two triangles are not congruent, then two sides and the included angle of one triangle are not congruent to two sides and the included angle of the other triangle (assuming this is the first option's text; adjust identifier if needed based on actual option labels, but from the analysis, this is the correct inverse statement)