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Teacher Notes

CONCEPT 1 – Prove theorems about triangles – The Side Splitting Theorem - A line parallel to one side of a triangle divides the other two proportionally.

 I love how this proof grows so naturally out of similar triangles. It is a natural progression from what we have just practiced.

CONCEPT 2 – Prove theorems about triangles – The Angle Bisector Theorem – An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

 Students will greatly struggle with this proof without the initial auxillary lines created. I like to discuss with them where the 'typical' similar triangle structure is in the new diagram. It usually gets them going in the right direction.

 There are many proofs of the Pythagorean Theorem..... but none are prettier than this one... It is a very simple and visual proof of the Pythagorean Theorem.

CONCEPT 3 – Prove theorems about triangles.  Prove the Pythagorean Theorem using triangle similarity.