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What is the converse of "If the triangle is isosceles, then only two of its sides are equal in length"?

a) If only two of a triangle's sides are equal in length, then it is isosceles.
b) If a triangle is not isosceles, then all of its sides are equal in length.
c) If a triangle's sides are not equal in length, then it is not isosceles.
d) If all of a triangle's sides are equal in length, then it is equilateral.

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Final answer:

The converse of the statement "If the triangle is isosceles, then only two of its sides are equal in length" is "If only two of a triangle's sides are equal in length, then it is isosceles." This is found in option (a).

Step-by-step explanation:

The student's question revolves around understanding the concept of the converse of a conditional statement in geometry. In this case, the original conditional statement is "If the triangle is isosceles, then only two of its sides are equal in length".

The converse of a conditional statement is formed by exchanging the hypothesis and conclusion of the original statement. Therefore, the converse of the given statement would be options (a) If only two of a triangle's sides are equal in length, then it is isosceles. This is because, in an isosceles triangle, by definition, exactly two sides have the same length.

Option (b) discusses a scenario of a non-isosceles triangle, which doesn't directly relate to the original statement's converse. Option (c) is stating the contrapositive of the original statement rather than its converse. Lastly, option (d) defines an equilateral triangle, which has all three sides of equal length, so this is not the converse either.

Understanding logical statements and their converse is crucial in mathematics to clearly express conditions and their logical implications.

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