Question

Write the following statement in five different ways conveying the same meaning.
P: If a triangle is equiangular then it is an obtuse angled triangle.

Answer 1

Hint: Here we use the general language links like ‘if, then, and, implies etc.’ to form five different statements that have the same meaning.

Complete step-by-step answer:
We are given the statement “If a triangle is equiangular then it is an obtuse angled triangle.”
We can write the given statement having same meaning as:
1) If a triangle is not an obtuse angled triangle, then it is not an equiangular triangle.
This statement has the same meaning as that of the given statement as it states the converse of the given statement.
2) A triangle is equiangular only if it is an obtuse-angled triangle.
This statement means that the triangle will be equiangular if the triangle is obtuse angled. So, this statement also has the same meaning as that of the given statement.
3) A triangle is equiangular implies that the triangle is an obtuse-angled triangle.
The word implies means that if the statement before the implication is true then the statement after the implication will also be true.
4) A triangle is equiangular only if it is an obtuse-angled triangle.
This statement is also a similar statement as the statement before the word ‘only if’ is the reason why the statement after the word ‘only if’ is true.
5) For a triangle to be equiangular, it is sufficient for the triangle to be an obtuse-angled triangle.
Since the word sufficient means that the condition that is sufficient or required to prove any statement, the above statement gives the same meaning as the given statement in the question.

Note: Keep in mind we have to keep the statement short and same but we can change the positioning and links joining the two statements within the statement.