In equilateral triangles all sides are equal. The inverse of the statement "An equilateral triangle has three congruent sides" is true.
What is an equilateral triangle?
An equilateral triangle is a triangle whose all sides are of equal length.
Given to us
Statement: An equilateral triangle has three congruent sides.
We know that an equilateral triangle has all three sides, if we look at the statement carefully, the statement can be divided into two parts, a condition, and a conclusion,
[tex]\rm \underbrace{\text{An equilateral triangle}}\ \underbrace{ \text{has three congruent sides}}[/tex]
Part one is the condition that the triangle must be an equilateral triangle, while part two is a conclusion that if the first condition is true then the sides of the triangles are congruent.
In order to inverse the statement, we need to inverse both the parts conclusion and the condition, therefore, the statement will be,
[tex]\rm \underbrace{\text{In an non-equilateral triangle}}\ \underbrace{ \text{Not all sides are congruent}}[/tex]
The inverse of the statement holds true, if a triangle is not an equilateral triangle then the triangle may have two sides congruent but not it is not possible that all the lines are congruent.
Hence, the inverse of the statement "An equilateral triangle has three congruent sides" is true.
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