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The intercept theorem is also known as thale's intercept theorem.

There can be different forms of this theorem shown in different figures.

Let us say that there are  two transverse lines T1 and T2, intersecting in a plane.  There are parallel lines. L1 and L2.  Then the line segments on  T1 and T2  cut by L1 and L2 are in proportions.

The line segments cut from L1 and L2  by T1 and T2 are also in proportions.

Suppose there is a third transverse line.  Then,  the ratios of the line segments cut on the parallel lines by the transverse lines are in proportions.

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