# Triangle similarity: Definition, criteria and demonstrations

- Author:
- Jorge Cássio

- Topic:
- Geometry, Similar Triangles, Triangles

## Definition

Two triangles are similar if and only if they have the three angles

**congruently arranged**. Also, the equivalent sides**must be proportional.**## Similar triangles

## Analysis 1

Change the positions of points A, B, C, A', B' or C'. What do you see regarding the value of k?

## Analysis 2

Change the positions of points A, B, C, A ', B' or C 'so that k is equal to 1. What can you notice about the triangles?

## 1st Similarity Case: ANGLE-ANGLE SIMILARITY

## 2nd Similarity Case: Side-Angle-Side

## Exercise

Find a reason for the use of theorem in the previous demonstration: "If a line divides two sides of a triangle and determines segments proportional to those two sides, then it is parallel to the third side." Use the following figure as reference.