When we have atriangle, we can identify that it is anisosceles if at least one of the following conditions is met:

1) If the triangle has two equal angles - The triangle is isosceles. 2) If in the triangle the height also bisects the angle of the vertex - The triangle is isosceles. 3) If in the triangle the height is also the median - The triangle is isosceles. 4) If in the triangle the median is also the bisector - The triangle is isosceles.

Before we talk about how to identify an isosceles triangle, let's remember that it is a triangle with two sides (or edges) of the same length - This means that the base angles are also equal. Moreover, in an isosceles triangle, the median of the base, the bisector, and the height are the same, that is, they coincide.

Let's see it illustrated

These magnificent properties of the isosceles triangle cannot prove by themselves that it is an isosceles triangle. So, how can we prove that our triangle is isosceles?

If at least one of the following conditions is met: 1) If our triangle has two equal angles - The triangle is isosceles. This derives from the fact that the sides opposite to equal angles are also equal, therefore, if the angles are equal, the sides are too.

2) If in the triangle the height also bisects the vertex angle - The triangle is isosceles. 3) If in the triangle the height is also the median - The triangle is isosceles. 4) If in the triangle the median is also the angle bisector - The triangle is isosceles. In fact, we can summarize guidelines $2$ and $4$ and write a single condition: If two of these coincide - the median, the height, and the bisector - The triangle is isosceles.

Great, now you know how to identify isosceles triangles easily and quickly.

If you are interested in learning more about other angle topics, you can enter one of the following articles: