A figure that can be folded over along a straight line so that the re

Question

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

(A) square

(B) circle

(C) equilateral triangle

(D) isosceles triangle

(E) rectangle

DavidTutorexamPAL · Answer

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).

ramblers · Answer

So D is obviously the right choice.

However...B is sort of tricky. With a circle of no markings (not a clock, not a compass, the top of a can, whatever)...just a circle...is any diameter different from another? With no relativity, isn't there just 1 diameter? I realize this is a tree falling in the woods scenario, but it was enough to give me some pause to think if this was some sort of trick question.

Masterscorp · Answer

Hi jsheppa , if you analyze the question and the answers it becomes clear that there can be different lines of symetry even if they have the same length. In a circle there is an infinite number of symetry lines. What makes it even clearer that if you analyze the rectangle and the square you see that they have two diagonals with the same length and that these function as two different symetry lines. If lines with equal length would be treated as one symetry lines, we would have atleast 3 answers with one symetry line, right? Hence, it is clear that different lines can have the same length. I hope that helps

A figure that can be folded over along a straight line so that the re

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