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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