Similarity of Triangles

Two figures are said to be similar, if they have the same shape but may differ in size.

Two triangles are said to be similar, if their corresponding angles are equal and their corresponding sides are proportional.

In similar triangles, the sides opposite to equal angles are said to be the corresponding sides.

In similar triangles, the angles opposite to proportional sides are said to be the corresponding angles.

SAS postulate: If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

AAA or AA postulate: If two triangles have two pairs of corresponding angles equal, then by the angle sum property of a triangle their third angle will also be equal and hence the triangles will be similar.

SSS postulate: If two triangles have their three pairs of corresponding sides proportional, then the triangles are similar.

Basic Proportionality Theorem:

A line drawn parallel to one side of a triangle divides the other two sides proportionally.

Conversely, if a line divides any two sides of a triangle proportionally, the line is parallel to the third side.

In a size transformation, a given figure is enlarged or reduced by a scale factor k such that the resulting figure is similar to the given figure.

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