What triangle has 0 reflectional symmetries?

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Question:

What triangle has 0 reflectional symmetries?

Answer:

I think your question must be “What triangle has 3 reflectional symmetries?”. Because there are given only three options, and all of them satisfy some rules to have reflectional symmetries. There is none triangle that has 0 symmetry. Let’s discuss it in detail :-

Rule 1 : A reflection symmetry must be a reflection line that bisects a figure such that they get folded on each-other across the reflection line.

Rule 2 : A reflection symmetry must pass through any vertex of the figure, and the sides intersecting at this vertex must be congruent sides.

Rule 3 : An equilateral triangle has three reflection symmetries as all sides are congruent and it is uniform from each vertex. Similarly, an isosceles triangle has only one reflection symmetry as it has only one pair of congruent sides.

Given option A is an equilateral triangle, so it has 3 reflection symmetries.

Given option B is an isosceles Right triangle, so it would have only 1 reflection symmetry.

Given option C is an isosceles triangle, so it would have only 1 reflection symmetry.

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It means option B and option C have same answer i.e. only 1 reflection symmetry. But option A has 3 reflection symmetries.

So question must be “What triangle has 3 reflectional symmetries?”. Therefore, option A would be correct in that case.

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