In Figure 81 one of the triangles is the original and the ot

In Figure 8.1, one of the triangles is the original, and the other three are the result of a translation, a rotation, and a reflection.

Write a paragraph explaining how you determined which triangle is which.

Solution

As there are four triangles, let us name them from 1 to 4 in the clockwise direction.
Given is that one triangle is the original and result are the result of translation, rotation and reflection.
From the figure we can see that triangles 2 and 3 look similar, hence one can be termed as original and the other one as translated triangle as to translate a figure is to simply slide it somewhere else. But in the move, you may not change the figure in any other way. You cannot rotate it, resize it, or flip it.
So triangle 2 is the original and triangle 3 is the flipped triangle.

If you see triangles 2 and 4, triangle 4 is in the exact opposite direction without any change in the angles w.r.t. to the three axis. Hence, triangle 4 is the reflection triangle of triangle 2.

Now consider triangles 1 and 2, if you rotate triangle 2 in anti clockwise direction you would be getting traingle 1. Therefore, triangle 1 is a result of rotation of original triangle 2.