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Subject: "geometry grade 12"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #337
Reading Topic #337
faisal
guest
Dec-12-05, 11:41 AM (EST)
 
"geometry grade 12"
 
   hi
i was lookin for converse of Hypotenuse-Side theorem on the net . i wasn't able to find it. i spent a full hour but no luck. this theorem is in my book and it makes sense . but how do i prove the converse of it. here is the theorem itself "if the hypotenues and one other side of a right angle triangle is equal to the hypotenues and other side of another right triangle , then triangles r congruent". i think the converse wud be "if 2 right triangles r congrurnt than the hypotenues and one other side of one right triangel is equal to hypotenues and one other side of the other triangle"
now i dono if it makes sense, please help me. n how do i prove the converse by indirect method.


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alexbadmin
Charter Member
1740 posts
Dec-12-05, 11:46 AM (EST)
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1. "RE: geometry grade 12"
In response to message #0
 
   >i think the converse wud be "if 2 right triangles r congrurnt
>than the hypotenues and one other side of one right triangel
>is equal to hypotenues and one other side of the other
>triangle"

You should give a thought to what being congruent means. In a sense, congruent figures are equal, except for their position in the plane, say. If two triangles are congruent, their corresponding sides, angles, as well as the perimeter and area and also the corresponding medians, angle bisectors, to mention just a few relevant elements, are equal.


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Thomas McGrath
Member since Jan-11-06
Jan-11-06, 11:54 AM (EST)
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2. "RE: geometry grade 12"
In response to message #0
 
   Well, knowing the hypotenuse & one side clearly fixes the length of the other side to only one value. This means that you know the length of all of the sides, so if the hypotenuse and one side of two triangles are equal, necessarily the other side must also be equal. All sides are equal therefore the triangles are congruent.


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alexbadmin
Charter Member
1740 posts
Jan-11-06, 11:59 AM (EST)
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3. "RE: geometry grade 12"
In response to message #2
 
   But what is the converse of the statement:

If the hypotenuse and one other side in two right triangles are equal, then the triangles are equal.

In my view, the converse is:

If two right triangles are equal then their hypotenuse and one other side are equal.

What does the third side have to do with that?


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