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I am in little fear to ask this question here, because I think it is very basic and I will understand it myself in some time but now I am getting serious trouble with directly and oppositely similar triangles which I mention below. ...

Note -I have already seen this question here Similar and directly similar figures but I am still uncomfortable with directly and oppositely similar triangles.

The problem is while solving a contest geometry problem one often has to see the 2 triangles are directly or oppositely similar , for ex in using complex bashing on a problem there are two formulas for areas of a given complex triangle depending on it is directly or oppositely(as mention in EGMO book) ...

But I am confused to decide which is directly or oppositely when a problem came in front of me,so can somebody provide a way to determine when two triangles are directly or oppositely similar ? (without using directed angles notations, I mean just by seeing the diagram of $2$ triangles, diagram with explanation will be greatly helpful)

thank you very much

Also i did not find any article on web that explain this ,so if someone can share a article then i will erase my question.

Bernard
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Ishan
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    Let sides $a,b,c$ in one triangle be proportional to sides $x,y,z$, respectively, in the other triangle. Go around the 1st triangle in the order $a,b,c$, and go around the 2nd in the order $x,y,z$. If you went clockwise one time and counterclockwise the other time, then the triangles are oppositely similar. Otherwise, they are directly similar. – Gerry Myerson Aug 21 '20 at 11:30
  • @GerryMyerson thankyou very much,now i am very clear with this,thanks again... – Ishan Aug 21 '20 at 15:25
  • as a note, it is very similar to concept of signed areas of a triangle.. – Ishan Aug 21 '20 at 15:27
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    I'm going to repost my comment as an answer. – Gerry Myerson Aug 22 '20 at 00:23

1 Answers1

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Let sides $a,b,c$ in one triangle be proportional to sides $x,y,z$, respectively, in the other triangle. Go around the first triangle in the order $a,b,c$, and go around the second triangle in the order $x,y,z$. If you went clockwise one time, and counterclockwise the other time, then the triangles are oppositely similar. Otherwise, they are directly similar.

Gerry Myerson
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