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Proof: Basic Proportionality Theorem for Triangles | Geometry
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If a line is drawn parallel to a side in a triangle, so that it intersects the other two sides in two distinct points, then those two sides are cut in the same ratio. This is the basic proportionality theorem for triangles, very related to similar triangles. It is also called the intercept theorem or Thale's theorem.
We'll prove this theorem in today's geometry lesson, making use of the fact that triangles with the same base between the same parallels have the same areas. This will allow us to construct equal ratios of areas of different triangles. Note, in the video, triangle ADE is similar to triangle EBC. This is because the triangles have equal angles (they share angle A, then B and D are corresponding angles on parallel lines, and similarly for E and C). Thus, not only is AD to DB as AE is to EC, but these ratios are also the same as the ratio of DE to BC.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
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+WRATH OF MATH+
Follow Wrath of Math on...
We'll prove this theorem in today's geometry lesson, making use of the fact that triangles with the same base between the same parallels have the same areas. This will allow us to construct equal ratios of areas of different triangles. Note, in the video, triangle ADE is similar to triangle EBC. This is because the triangles have equal angles (they share angle A, then B and D are corresponding angles on parallel lines, and similarly for E and C). Thus, not only is AD to DB as AE is to EC, but these ratios are also the same as the ratio of DE to BC.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
********************************************************************
+WRATH OF MATH+
Follow Wrath of Math on...
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