Question

a statement is shown. if the base angles of a triangle are congruent, then the triangle is an isosceles triangle. which is the inverse of the statement? ○ if a triangle is an isosceles triangle, then the base angles of a triangle are congruent. ○ if the base angles of a triangle are not congruent, then the triangle is an isosceles triangle. ○ if a triangle is not an isosceles triangle, then the base angles of the triangle are not congruent. ○ if the base angles of a triangle are not congruent, then the triangle is not an isosceles triangle.

Explanation:

Step1: Recall the definition of inverse of a conditional statement

A conditional statement is in the form "If \( p \), then \( q \)". The inverse of this statement is "If not \( p \), then not \( q \)".

Let \( p \) be "the base angles of a triangle are congruent" and \( q \) be "the triangle is an isosceles triangle".

Step2: Apply the definition to the given statement

The original statement is "If \( p \), then \( q \)". So the inverse should be "If not \( p \), then not \( q \)".

• "not \( p \)" is "the base angles of a triangle are not congruent"
• "not \( q \)" is "the triangle is not an isosceles triangle"

So the inverse statement is "If the base angles of a triangle are not congruent, then the triangle is not an isosceles triangle".

Answer:

If the base angles of a triangle are not congruent, then the triangle is not an isosceles triangle. (The fourth option)