Question

select the statement that is the contrapositive of the following statement:
if a triangle is isosceles, then it has congruent base angles.
answer

• if a triangle has congruent base angles, then it is isosceles.
• if a triangle doesnt have congruent base angles, then it isnt isosceles.
• if a triangle is isosceles, then it doesnt have congruent base angles.
• if a triangle isnt isosceles, then it doesnt have congruent base angles.

Explanation:

Step1: Recall contrapositive definition

The contrapositive of a conditional statement \( p \to q \) (where \( p \) is the hypothesis and \( q \) is the conclusion) is \(
eg q \to
eg p \).

Step2: Identify \( p \) and \( q \)

For the statement "If a triangle is isosceles, then it has congruent base angles", \( p \): "a triangle is isosceles", \( q \): "it has congruent base angles".

Step3: Find \(

eg q \) and \(
eg p \)
\(
eg q \): "a triangle doesn't have congruent base angles", \(
eg p \): "it isn't isosceles".

Step4: Form contrapositive

Using \(
eg q \to
eg p \), the contrapositive is "If a triangle doesn't have congruent base angles, then it isn't isosceles".

Answer:

If a triangle doesn't have congruent base angles, then it isn't isosceles.