then angle TSQ is congruent to angle RQS
as they are both the third angle needed to form the triangle.
then triangles TQS and RSQ are symmetric.
but also QS is equal to SQ
thus the triangles are not only symmetric they are also congruent.
all corresponding angles are equal and one corresponding side is already equal. this will also make the other corresponding sides equal also.
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2007-11-11 10:41:53
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answer #1
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answered by Alam Ko Iyan 7
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What I'm picturing here is a quadrilateral (QRST), with a line through the middle..from point Q to point S. If I'm right in assuming this, then the answer is actually pretty simple. I' m including a diagram and I know it's obviously not perfect but it gives you somewhat of a visual of what I mean..
So anyways, you already know that T and R are congruent, and you know that TQS is congruent to RSQ. So therefore SQR must be congruent to QST, as there are 180° in any triangle and you already know that two out of three in each are the same. This proves that the angle measures have to be equal, but if you think about it, the sides have to correspond as well because the triangles are connected and the angles are the same. I don't know how to put it into words exactly, but if you draw it out any way you want, you will see that it isnt possible! I hope this helped..sorry it was so long =]
Also, you never actually said that the triangles were connected. If they aren't, you can only prove they are similar, not congruent. Once again, hope this was helpful.
And here is the link to my diagram..it's not very good ;]
http://i19.tinypic.com/854m789.jpg
2007-11-11 18:54:28
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answer #2
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answered by Mariee 4
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Hi, I could be wrong, but here goes: Is the drawing of the two triangles a square, whereby they both share side qs? And is it a perfect square, so that angle QT S is a 90 degree angle and angle QRS is a 90 degree angle? If so, then Postulate 15 should appy, which states: if two angles and the side between them are congruent then the third angles are congruent, and the two triangles are then congruent. Check your geometry book. let me know how lyou make out!
2007-11-11 18:59:14
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answer #3
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answered by Marcia X 3
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From rhe given data it is clear that both the triangles TQS and RSQ are on the same base QS.
m
m
QS = QS (common base)
so triangles are congruent (AAS)
2007-11-11 18:45:07
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answer #4
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answered by mohanrao d 7
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you already have two congruent angles, you only need one congruent sides, which is qs and sq (reflective)
so use AAS as reason for congruent triangles.
2007-11-11 18:35:16
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answer #5
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answered by norman 7
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well if t is equal to r and q is equal to q and s is equal to s then that means the all angles equals eachothers congruent angles
2007-11-11 18:32:13
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answer #6
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answered by Kenny 3
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its hard to visualize the figure
2007-11-11 18:31:58
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answer #7
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answered by CPUcate 6
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flcik
2007-11-11 18:38:47
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answer #8
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answered by Stuck 3
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