doubt in congruency of triangle?

Question

here is the definition of congruent triangle in my book

http://img262.imageshack.us/my.php?image=congruent3qm.jpg

i have a question on it.

there are 6 statements , for example a,b,c,d,e,f .

Q1; my question is , if at least one of them is satisfied , then can we call 2 triangles are congruent ? or the 2 triangles must have to satisfy ALL the above conditions ? which is correct ?


Q2; please look at condition (d)...

it says
but if i change this to ,
please note ,i have just changed the ordering of side in the above .....I am not sure whether i still would be able to call these triangles as congruent ....does the change of ordering like above affect at all ?.......please clarify this doubt.

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Mr jason ,please note .... i have chosen another side for comparison NOT the side stated in the book ( for condition d) and hence i am not sure that whether i could enjoy that freedom .. am i flexible with that ?

Answer 1

1) If you can show that a triangle satisfies one of the conditions, the others necessarily follow from that.

2)You are simply restating the proposition with a different side. Thus, it holds as well

Answer 2

If all 3 angles are identical, the triangles may be only similar and not congruent.

Similar triangles have same shape and different sizes.

(3 sides on the other hand does define congruent triangles.)

Your teacher should have explained better than that web link and I think you should ask him or her to go through it again. The web link contains too much info and too little clarity.

Answer 3

some triangles are no longer categorised thoroughly to make you prepare your different instructions on geometry. All you're able to do is attempt to ascertain what the relationships or lengths of two or 3 aspects and/or angles, reckoning on the conjecture you're finding out. as an occasion, if it says "M is the midpoint of the two triangles", then M could be dividing an somewhat long section crossing the two triangles into 2 smaller segments. each and every of those smaller segments could be performing as aspects to distinctive triangles. via the definition of midpoint, those smaller segments are additionally congruent segments because a midpoint divides segments the two. because those are additionally aspects, then you certainly can end that this pair of aspects which variety an somewhat long section whose midpoint is M are congruent.

Answer 4

the answer is NO..

if you changed the ordering of the side, it lacks information..


if you changed the sides AB=XY, then it should be ,