Proof: SAS Similarity Theorem

Proving -- SAS Similarity Theorem: If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar.

[mzmagenta]

Thank you! I have been looking everywhere for the proof of this theorem.

[carter]

This proof is wrong. You can NOT construct a line XY parallel to BC and construct AX = DE, AY = DF at the same time. All you did was assume that they were similar and then said they were similar because of what you assumed. That's not how a proof works.

You should construct the point X on AC such that DF = AX and then construct the line l such that X is in l and l is parallel to BC.
Let Y be the point of intersection of l with AB. Then you know AX/AB = AY/AC (By Parallel Projection).
Then, you use the ratios given to come to the conclusion that all the corresponding angles are congruent.

[anniezhao]

THIS IS WRONG. How could you substitute DF with AY? There is no information saying that the ratios are the same. 😅

[daniellee]

sigh every single proof has itself to prove itself. it makes no sense. u can't prove itself with itself omg

[teacherhimself]

thanks so much, my teacher sucks at teaching

[jmsaberonn]

it cant be read your handwritten, it was too hard to understand