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File:Lexell's theorem via a Saccheri quadrilateral.png

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English: Lexell's theorem can be proved using a Sacherri quadrilateral ABB'A'. If m is the line connecting the midpoints M1 and M2 of sides AC and BC, let A', B', and C' be the perpendicular projections of the triangle vertices onto m. Then the red triangles AA'M1 and CC'M1 are congruent, as are the blue triangles BB'M2 and CC'M2. Therefore the area of triangle ABC is equal to the area of Sacherri quadrilateral ABB'A'. Plotted with Desmos. Interactive version: https://www.desmos.com/geometry-beta/oihbmn4rc6
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Author Jacob Rus

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Lexell's theorem can be proved using a Sacherri quadrilateral ABB'A' of the same area as the triangle ABC.

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27 June 2023

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Date/TimeThumbnailDimensionsUserComment
current19:08, 9 July 2023Thumbnail for version as of 19:08, 9 July 20231,226 × 1,226 (404 KB)Jacobolusmark right angles
02:14, 30 June 2023Thumbnail for version as of 02:14, 30 June 20231,224 × 1,224 (366 KB)Jacobolusrelatively larger labels
20:00, 27 June 2023Thumbnail for version as of 20:00, 27 June 20231,856 × 1,856 (809 KB)JacobolusUploaded own work with UploadWizard

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