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\begin{tabular}{l} True or false? Isosceles triangles are equilateral triangles. \\ Select the correct answer \\ True \\ \hline False \\ \hline\end{tabular}

Ask by Bates Parry. in the United States
Feb 25,2025

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Answer

Isosceles triangles are not always equilateral triangles.

Solution

To determine whether the statement "Isosceles triangles are equilateral triangles" is true or false, let's analyze the definitions of both types of triangles: 1. **Isosceles Triangle**: A triangle with at least two sides of equal length. This means that an isosceles triangle can have two sides that are equal, while the third side can be of a different length. 2. **Equilateral Triangle**: A triangle where all three sides are of equal length. This is a specific case of an isosceles triangle, where not only two sides but all three sides are equal. Given these definitions, we can conclude that while all equilateral triangles are isosceles (since they have at least two equal sides), not all isosceles triangles are equilateral (since they can have two equal sides and one different side). Therefore, the statement "Isosceles triangles are equilateral triangles" is **False**.

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The Deep Dive

False! An isosceles triangle is defined as having at least two sides of equal length, while an equilateral triangle has all three sides of equal length. This means that while all equilateral triangles are indeed isosceles (because they meet the two-side criteria), not all isosceles triangles qualify as equilateral. To further clarify, consider the famous example of the isosceles triangle: the classic "A-frame" roof shape! In real life, many structures utilize isosceles triangles for stability, like bridges and towers. Meanwhile, the rigid structure of equilateral triangles can be seen in things like trusses, offering great strength and support. Triangles truly are the unsung heroes of both geometry and engineering!

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