Step 1: Note down all types of the triangles.

NOTE: Types of triangles

1) Isosceles triangles

2) Equilateral triangles

3) Scalene triangles

Step 2: Check the similarity principle with isosceles triangle

DEFINITION: Two figures are **similar** means that they share a common

shape. They can be different sizes, but they must have the same shape.

NOTE: Isosceles triangles are not always similar.

EXPLANATION:

For two triangles to be similar the angles in one triangle must have the same values as the angles in the other triangle. The sides must be proportionate.

Both may be isosceles but one could have angles of 30°, 30°, 120°

and the other could have 20°, 20°, 140°. Hence it is not always true that isosceles triangles are similar.

Step 3: Check the similarity principle with equilateral triangle.

NOTE: All equilateral triangles are similar.

EXPLANATION: A property of equilateral triangles includes that all of their angles are equal to 60 degrees.

The AAA Triangle similarity Postulate states that if all of the angles in a triangle are equal to the corresponding angles in another triangle, then those two triangles are equal.

Since every equilateral triangle's angles are 60 degrees, every equilateral triangle is similar to one another due to this AAA Postulate.

Step 4: Check the similarity principle with scalene triangle.

NOTE: Two scalene triangles are not similar triangles because in two triangles corresponding angles are not congruent and also all three corresponding sides of two triangles are not proportional to each other.