Proof: Basic Proportionality Theorem for Triangles | Geometry
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- เผยแพร่เมื่อ 23 ส.ค. 2024
- 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.
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Very much thank you!!.....I was so confused in this proof ...You are amazing
You're very welcome! I'm glad to hear it helped and let me know if you ever have any video requests!
You are a really good teacher Sir! I just wrote my board exam and this is EXACTLY what came in the exam. I remembered it so well i completed the whole proof in 5 mins 😂😂.
Thank you so much for the video. I will definitely be keen to check on future lessons!
Love from India sir
Boards kaisa gya bhai
thank you sm!!!!!!!! the explanation was amazing and rlly easy to understand
Glad to help!
Beautiful, just beautiful 🥲
Thank you!
Its gone very helpfull to me thanks 🙏
So glad it was helpful! Thanks for watching!
Hello, could you prove the 3rd equality ? DE/BC = AE/EC ?
Beautiful
Thank you!
Thanks sir
No problem, thanks for watching and for the request!
Thanks Lot !!!
My pleasure!
Hello I have a question I think the proof has a problem you drew altitude from point E to AD but what if there is an acute angle that is an gone bigger than 90 degrees then you can’t draw inner altitudes so this assumption is wrong
Thanks for watching and for your question! I just looked at the proof briefly to see your question, so I could be wrong - but I'm pretty sure we never use the assumption that the altitude EP falls inside of the triangle. What's important is that it intersects line AB, it's the distance from that line to point E, and this is the height of two of our triangles. By the line AB I mean if we were to continue segment AB infinitely in either direction to create a line. If angle A is obtuse, then like you say the altitude from E will fall outside of the triangle, but that doesn't break anything in the proof, it would just make us have a slightly uglier diagram. Hope that helps!
WOW!
This must be the first Math teacher who talks a lot, too much for an intro bro
You just help me on subset thank you
Glad to hear it! Thanks for watching!