alternate proof of parallelogram law
Proof of this is simple, given the cosine law:
where , , and are the lengths of the sides of the triangle, and angle is the corner angle opposite the side of length .
Let us define the largest interior angles as angle .
Applying this to the parallelogram
, we find that
Knowing that
we can add the two expressions together, and find ourselves with
which is the theorem we set out to prove.
Title | alternate proof of parallelogram law |
---|---|
Canonical name | AlternateProofOfParallelogramLaw |
Date of creation | 2013-03-22 12:43:52 |
Last modified on | 2013-03-22 12:43:52 |
Owner | drini (3) |
Last modified by | drini (3) |
Numerical id | 5 |
Author | drini (3) |
Entry type | Proof |
Classification | msc 51-00 |
Related topic | ProofOfParallelogramLaw2 |