Reflections?

Question

what are 2 polygons other than a square and a rectangle whose reflections are identical to the original. Show how the reflectin of a triangle can be the same as the original.

I dont understand this question, Help! Thanks in advance!!!!!!!!

Answer 1

I think this question is about handedness. The reflection of a grand piano, for example, is not identical to the original, because the curve will appear to be on the opposite side of the keyboard.

But the reflection of ANY regular polygon (i.e., with equal sides and inscribed in a circle) is the same as the original. In fact, ANY figure is identical to its reflection IF the figure has a line of symmetry -- meaning that if you put the mirror on that line, the reflection will coincide with the part of the figure behind the mirror.

E.g. the reflection of the letter D or E is identical to the original. since they both have a horizontal line of symmetry. However, p turns into q when reflected, because it has no symmetry about a line. (I know D and E aren't polygons, but the idea is actually more general.)

And so the reflection of an ISOSCELES triangle is the same as the original, since it has a line of symmetry, namely the altitude drawn above the base.

Answer 2

The previous answer was good.

Basically, there are many polygons such that there are one or more axes of symmetry, where an axis of symmetry is a line such that, if you reflect the original polygon in it, you get an identical copy.

In particular, consider a regular hexagon, and any of the three lines that connect diametrically opposite vertices. Or the regular octagon, and any of the four lines that connect diametrically opposite vertices. Or an equilateral triangle, and a line that passes through a vertex and bisects the opposite side. Or for that matter an isocecles triangle, and a line that passes through the apex and bisects the opposite side. Or any rhombus (not just a square), and a line that connects opposite vertices.

Each of the lines I mentioned is an axis of symmetry for the respective polygon.