Bunuel wrote:

A figure that can be folded over along a straight line so that the result is two equal halves which are then lying on top of one another with no overlap is said to have a line of symmetry. Which of the following figures has only one line of symmetry?

(A) square

(B) circle

(C) equilateral triangle

(D) isosceles triangle

(E) rectangle

Since this is a very 'visual' / graphic question (and also an uncommon question), we'll either try drawing it out or just guess.

This is an Alternative approach.

Drawing a square, we can SEE that the diagonal is a 'symmetry line' as defined above:

if splits the square into two identical halves that fall exactly one on top of the other.

(A) is eliminated.

(B) is also eliminated as every diameter is a symmetry line.

(C) is eliminated as every one of the heights also splits the triangle into two identical halves.

(D) is a bit trickier so we can skip it and look at E.

(E) also has two symmetry lines: these are the lines connecting the midpoints of the sides.

So (D) must be our answer.

(It does, in fact, have only one line. If AB = AC then the height from A to BC is the only line).

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