SOLUTION: If triangle ABC is a triangle such that a^2 + b^2 = c^2, then angle BCA is a right triangle? This is the converse to the Pythagorean Theorem. Please do not use law of cosine!

Algebra ->  Algebra  -> Geometry-proofs -> SOLUTION: If triangle ABC is a triangle such that a^2 + b^2 = c^2, then angle BCA is a right triangle? This is the converse to the Pythagorean Theorem. Please do not use law of cosine!      Log On

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Question 192713This question is from textbook
: If triangle ABC is a triangle such that a^2 + b^2 = c^2, then angle BCA is a right triangle? This is the converse to the Pythagorean Theorem. Please do not use law of cosine!This question is from textbook

Answer by jojo14344(1483) About Me  (Show Source):
You can put this solution on YOUR website!


If triangle ABC has dimensions , we want to prove angle BCA is a Right Triangle.

Remember a Square is formed by four Right Triangles, being each triangle has the same dimensions as the other triangles.


See figure below:


We get the Area of the outer Square:

Also,


*Note: ----> Area of 4 Right Triangles outside the inner square.

Therefore,






Then, Triangle ABC has sides

---> Angle BCA is Right Triangle

Thank you,
Jojo