Question

Write the converse, inverse, and contrapositive of the statement "If a triangle is equilateral, then it is equiangular."

Answer 1

"If a triangle is equilateral, then it is equiangular."

• p = A triangle is equilateral.
• q = A triangle is equiangular.

1. Converse:
   • Statement: If a triangle is equiangular, then it is equilateral.
     Form: q → p
   • Explanation: The hypothesis and conclusion are swapped in the converse.
2. Inverse:
   • Statement: If a triangle is not equilateral, then it is not equiangular.
   • Form: ¬ p → ¬ q
   • Explanation: The negation of both the hypothesis and conclusion.
3. Contrapositive:
   • Statement: If a triangle is not equiangular, then it is not equilateral.
   • Form: ¬ q → ¬ p
   • Explanation: The negation of both statements, with their order swapped.