questions on similar triangle

defeated_soldier

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Apr 15, 2006
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this is a question based on two triangles similarity. in order to make you understand my question i have written down 2 triangles in a piece of paper.

http://img476.imageshack.us/my.php?imag ... glega6.jpg

can we say , in fig 1 (1) and (2) are similar triangle ? important point is , they have the same angles but they are RELATIVE , not in correspondence . so, i hesitate to take a decision whether they are elligible to be called as similar triangles . Does relative position matters ? see , both the triangles have 40, 40 and 100 degree ......but they are not in correspondence.

same thing (3) and (4) for measure in side ...they are gaving same sides but they are in relative not in correspondence ....can we call (3) and (4) as similar triangles ?

Please see , my drawing are not good ....but at least i am trying to make you understand where is my doubt and my question......if you have an answer , please provide that ..

thank you
 
defeated_soldier said:
in order to make you understand my question i have written down 2 triangles in a piece of paper.

http://img476.imageshack.us/my.php?imag ... glega6.jpg
Your triangles are not drawn to scale, which may make basing any decision about similarity on appearances unreliable.

In triangle 1, call one of the 40-degree angles A, the second 40-degree angle B, and the 100-degree angle C. In triangle 2, call one of the 40-degree angles D, the second 40-degree angle E, and the 100-degree angle F. Would you agree that it is possible to match up the angles in the following way?
A <-> D
B <-> E
C <-> F
Because we have three pairs of corresponding angles which are congruent, the triangles are similar by the AA(A) similarity theorem.

If you draw more accurate diagrams, showing two triangles each with two 40-degree and one 100-degree angles, I think you'll be able to convince yourself that the triangles are indeed similar.

On the second problem, regardless of the way the triangles LOOK in the diagram, if the segments labeled the same way (x, y, and z) are in fact the same size, then the triangles are not only similar but congruent (By the SSS Similarity Theorem and the SSS Congruence Postulate). Do not let yourself be fooled by appearances.

Go with what you KNOW to be true, not what LOOKS to be true. We can make no judgments about things like lengths and angle measures based on the appearance of a diagram.
 
yea, i agree my drwaing is not in the scale .

what i was asking is , does the relative position impacts triangular similariry ?

suppose,ok , let me ask other way , suppose i have triangle 1 and triangle 2 .....and they are similar . if i rotate the triangle 2 in clockwise direction ........can i still be able to call triangle 1 and triangle 2 are similar ..............because they will look differently and in that case it would be very difficult to MATCH UP angles/ sides in correspondence...........so, can we call these triangles are similar .

In my question , thats why i changed the angle to disturbe the correspondence rule (of course the scale and looks would be different but lets forget that).....and asked whether i can call these as similar triangles ?
 
Go with what you KNOW to be true, not what LOOKS to be true. We can make no judgments about things like lengths and angle measures based on the appearance of a diagram.
oh, i see ...thats a very good comment ...in fact i wanted to know this........very nice .........ok so then why the rule of similarity talks about "correspondence rule" if the appearence does not matter ......this particular keyword should be removed from the definition.[/quote]
 
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