Triangle similarity: Definition, criteria and demonstrations

Definition
Two triangles are similar if and only if they have the three angles [b]congruently arranged[/b]. Also, the equivalent sides [b]must be proportional. [/b]
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
[br][br]Find a reason for the use of theorem in the previous demonstration: "If a line divides two sides of a triangle[br]and determines segments proportional to those two sides, then it is parallel to the third side." Use the following figure as reference.[br][br][img]https://cdn.geogebra.org/material/qmJyXBAamZbl9s7GoEh5QSsjwL5q4S7V/material-Pxxtb5RS.png[/img]
3rd Similarity Case: Side-Side-Side (SSS)
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Information: Triangle similarity: Definition, criteria and demonstrations