A square has symmetry with respect to a line containing a median of the square.
True
False
true?
False.
A square has symmetry with respect to a line passing through both the center and any two opposite vertices (one of which is the midpoint of a side), not a median.
That is correct, the statement is true.
To understand why a square has symmetry with respect to a line containing a median of the square, let's first define what symmetry means. In geometry, symmetry refers to a property of an object or shape that remains unchanged under some transformation.
A square has four medians, which are line segments that connect each vertex of the square to the midpoint of the opposite side. These medians divide the square into four congruent triangles.
If we draw a line containing one of the medians, it will pass through the vertex of the square and the midpoint of the opposite side. This line will divide the square into two congruent halves. In other words, if we fold the square along this line, the two halves will perfectly overlap each other.
This folding operation is an example of a transformation called reflection, where an object is flipped across a line. In this case, the line containing the median acts as the line of reflection.
Therefore, a square has symmetry with respect to a line containing a median because it can be folded along that line to create two congruent halves.
Hence, the statement "A square has symmetry with respect to a line containing a median of the square" is true.