Basic Proportionality Theorem (Visual proof with Animation)

Basic Proportionality theorem was introduced by a famous Greek Mathematician, Thales, hence it is also called Thales Theorem. According to him, for any two equiangular triangles, the ratio of any two corresponding sides is always the same. Based on this concept, he gave theorem of basic proportionality (BPT). This concept has been introduced in similar triangles. If two triangles are similar to each other then,

i) Corresponding angles of both the triangles are equal
ii) Corresponding sides of both the triangles are in proportion to each other

Theorem:- If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

According to this theorem, if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

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