Конспект: перетворення подібності зберігають кути але змінюють довжини і площі

A similarity transformation is a composition of a rigid motion (congruence transformation) and a dilation. (In other words, we apply the rigid motion, followed by the dilation, or the other way around.)

We know that rigid motions preserve angles (by definition), as do dilations.

So when we "mix/combine" (i.e. compose) these two types of maps together, we get maps that still preserve angles. So similarity transformations also preserve angles.

(However, they do not preserve distances: while congruence transformations preserve distances by definition, almost all dilations do not—think about a magnifying glass, scale drawing, microscope, or telescope.)

Remember the intuition for similarity, same shape, different size. Since the shape is the same, the angles remain congruent. Since the size is different, the side lengths are in proportion.