Question

jeff asks the teacher if ASA is also a similarity criterion. The teacher says yes but it isn't needed, why isn't it needed ?

Answer 1

The reason for this is explained below :

Explanation:

For showing any two triangles similar, we need to show their corresponding sides are proportional to each other

So, to showing proportional or for taking ratio, minimum number of sides required are two which implies for showing any two triangles similar to each other we need to take minimum two sides.

But in ASA similarity criterion, there is only one side so we cant take proportion of the sides in this.

Hence, the teacher says right that it is sufficient to show any two angles equal for showing any two triangles similar, and we don't need to take any side.

Answer 2

ASA means that we have two angles and the lenght of the side between them.

But as you know, the sum of the 3 interior angles of a triangle must add up to 180°

So ASA is equivalent to the AA criterion (where we know two interior angles), with only knowing two angles we have enough to see if two triangles are similar, so actually knowing the length of the side is not needed.