Similarity of triangles-Similarity criteria

Similarity of triangles-Similarity criteria #geometry #mathematics #triangle
SIMILARITY OF TRIANGLES
Two triangles are similar when they have the same shape, regardless of size, position, or orientation.
This similarity is due to the fact that the internal angles of one are identical to the internal angles of the other, that is, their internal angles are congruent, consequently the homologous sides of one and the other triangle are proportional, that is, they will have the same geometric ratio.
Triangle ABC is similar to triangle RST.
If its internal angles are congruent to each other, remember that it is customary in geometry to speak of congruence instead of equality for geometric figures, since these are not quantities. Then their homologous sides, that is, their common sides keep the same proportionality or geometric ratio.
Thus we have that the geometric ratio of side AB to side RS is equal to the geometric ratio of side BC to side ST, and also equal to the ratio of side AC to side RT.
And vice versa, If the homologous sides are equal, the homologous interior angles are congruent.
If two triangles are similar, they are homologous, and obviously also proportional and comparable, the notable lines that start from the vertices of their internal angles, the radii of the inscribed, circumscribed, ex-inscribed circles, etc.
Cases of similarity of triangles.
A) First case
When two interior angles of a triangle are respectively congruent to two interior angles of
another triangle, then these triangles are similar:
B) Second case
When an interior angle of one triangle is congruent to another interior angle of another triangle and, in addition,
the sides that comprise these angles are proportional, then both triangles are similar:
C) Third case
When the three sides of one triangle are respectively proportional to three sides of another triangle,
then these triangles are similar.
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[@roniergrabielmarchanaponte489]

Buen contenido para el aprendizaje

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exceente....se entiende claro...los sigo...

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Gracias por la explicación bien detallada, entendí todo.

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Excelente