What do you mean by the Thales theorem class 10?

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Detailed Solution

Thales' Theorem (also known as the Basic Proportionality Theorem (BPT)) is a fundamental concept in geometry that is introduced in Class 10.

Thales' Theorem Statement:

If a line is drawn parallel to one side of a triangle, intersecting the other two sides, then it divides those two sides in the same proportion.

Mathematical Representation:

If in triangle ABC, a line DE is drawn parallel to side BC and intersects the other two sides AB and AC at points D and E, then:

(AD/DB) = (AE/EC)

Where:

AD and DB are the segments of side AB
AE and EC are the segments of side AC

Explanation:

The theorem states that when a line is parallel to one side of a triangle, the two sides it intersects are divided into proportional segments. This means the ratio of the lengths of one side is equal to the ratio of the lengths of the other side. It is often used to prove the similarity of triangles and solve various geometrical problems.

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