My math book tells me that two triangles are similar if all angles are equal to each other ("Angle-Angle-Angle (AAA) Similarity"). There are 4 rules summed up for similarity, I summarised them:
Angle-Angle (AA) Similarity. 2 pairs of angles are equal, so the third pair is equal too.
Side-Side-Side (SSS) Similarity. The ratio between all corresponding sides is constant.
And now the last two, of which I want to know why these rules are true. The two above are obvious for me, but these ones not.
Side-Angle-Side (SAS) Similarity. One angle is the same in both triangles, and the ratio between the sides around the angle is the same.
Hypotenuse-Leg (HL) Similarity. In a right triangle, the ratio between the hypotenuses and between two other are equal.
Can anyone explain 3 and 4?
Lastly, if you have 2 rectangular triangles, and the ratio between the sides around the right angle is the same, they must be similar, correct? Because the third rule applies on this.