Parallelograms in Geometry - II: What is Varignon's parallelogram theorem?

In this video, we answer the following questions only using midpoint theorem and properties of parallelograms.
What is Varignon's theorem?
What are medians?
Why are medians of a triangle concurrent?
Why does the point common to all medians (the centroid) trisect all the medians?
We chart out a natural path to Varignon's theorem by gluing two midpoint theorem configurations. Then Varignon's theorem naturally reveals the reason centroids exist. In other words, we prove medians of a triangle are concurrent via an exploration involving Varignon's theorem. Along the way, the properties of parallelograms expose the centroid's central property of trisecting all medians.
00:09 Recall Midpoint theorem
00:22 Gluing two Midpoint theorem configurations
01:57 Varignon's theorem on parallelograms
03:03 The definition of a median
03:24 Varignon's theorem in the Midpoint theorem configuration
03:45 Proof that centroid divides median in the ratio 2:1 (conclusion at 4:39 )
04:48 Proof of concurrency of median.
In the next video, we will build on the central property to prove altitudes are concurrent.
This video is a part of the parallelogram series. The series is a foundational material for school curriculum, Olympiad preparation. It will help students who are preparing for olympiad exams like IOQM, RMO, INMO, AMC, AIME, USAMO, IMO and some of the basics are helpful for IIT-JEE and other competitive exams.