Question

read the statement:
\if a triangle is isosceles, then its base angles are congruent.\
which statement is the contrapositive of the statement shown?

• if the base angles of a triangle are not congruent, then the triangle is not isosceles.
• if a triangle is isosceles, then its base angles are not congruent.
• if the base angles of a triangle are congruent, then the triangle is isosceles.
• if a triangle is not isosceles, then its base angles are not congruent.

Explanation:

To find the contrapositive of a conditional statement \( p \to q \), we negate both the hypothesis and the conclusion and then reverse their order, resulting in \(
eg q \to
eg p \).

The original statement is "If a triangle is isosceles (\( p \)), then its base angles are congruent (\( q \))", so \( p \): "a triangle is isosceles", \( q \): "its base angles are congruent".

Negating \( p \) gives \(
eg p \): "a triangle is not isosceles", and negating \( q \) gives \(
eg q \): "its base angles are not congruent".

Reversing the order of the negated statements gives the contrapositive \(
eg q \to
eg p \), which translates to "If the base angles of a triangle are not congruent (\(
eg q \)), then the triangle is not isosceles (\(
eg p \))".

Answer:

A. If the base angles of a triangle are not congruent, then the triangle is not isosceles.