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  1. All triangles are similar.
    (A) equilateral
    (B) isosceles
    © scelene
    (D) right-angled

Ask by Goodwin Harris. in India
Jan 22,2025

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All equilateral triangles are similar to each other.

Solución

To determine which type of triangle is similar to all others, we need to understand the properties of triangle similarity.
  1. Equilateral Triangles: All sides are equal, and all angles are 60 degrees. Any equilateral triangle is similar to any other equilateral triangle because they have the same shape and angle measures.
  2. Isosceles Triangles: These triangles have at least two equal sides. While isosceles triangles can be similar to other isosceles triangles with the same angle measures, they are not necessarily similar to all other triangles.
  3. Scalene Triangles: These triangles have all sides of different lengths. Similarity among scalene triangles depends on the angles. Not all scalene triangles are similar to each other.
  4. Right-Angled Triangles: Right-angled triangles can be similar if they have the same angle measures, but they are not similar to all triangles.
Based on this analysis, the only type of triangle that is similar to all others is:
(A) equilateral.
All equilateral triangles are similar to each other regardless of their size.

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Mind Expander

All equilateral triangles are similar because they have equal angles, which means any equilateral triangle you draw will be proportional to another, no matter the side lengths. Imagine trying to fit them together like puzzle pieces—every one will always match up perfectly!
On the other hand, isosceles triangles aren’t automatically similar just because they have two equal sides. They can have different angles and side lengths, meaning two isosceles triangles might not fit together as perfectly as their equilateral cousins. So, remember that similarity thrives on those equal angles!

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