https://www.khanacademy.org/math/class-10-geometry-od/x6c43792871149241:construction/x6c43792871149241:division-of-line-segment/v/division-of-a-line-segment-thales-theorem 2026-03-11T10:11:27.775666738Z Division of a line segment (Thales theorem) In this video, we explore how to divide a line segment in a specific ratio using Thales’ Theorem—without measuring the line directly. We begin by visualizing the challenge and recalling the statement of Thales’ Theorem, which lays the foundation for our construction. Step by step, we demonstrate how to draw an auxiliary ray, mark equal divisions, and connect key points to achieve the desired ratio. Each construction move is carefully justified using geometric reasoning, making the process both logical and elegant. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Division of a line segment (Thales theorem) In this video, we explore how to divide a line segment in a specific ratio using Thales’ Theorem—without measuring the line directly. We begin by visualizing the challenge and recalling the statement of Thales’ Theorem, which lays the foundation for our construction. Step by step, we demonstrate how to draw an auxiliary ray, mark equal divisions, and connect key points to achieve the desired ratio. Each construction move is carefully justified using geometric reasoning, making the process both logical and elegant. https://cdn.kastatic.org/ka-youtube-converted/ctnXxVRU_gc.mp4/ctnXxVRU_gc.mp4 313 Division of Line Segment