Question 669873
In the isosceles right triangle ᐃABC, AB=10 feet. what is the length of AC?

<pre>
That depends on how the vertices of the triangle are labeled.

If the triangle is labeled like this:

{{{drawing(200,200,-1,11,-1,11,triangle(0,0,0,10,10,0),
rectangle(0,0,1,1), locate(0,0,B), locate(0,10.8,A), locate(10,0,C),
locate(-1,5,10)


 )}}} then BC is also 10 feet {{{drawing(200,200,-1,11,-1,11,triangle(0,0,0,10,10,0),
rectangle(0,0,1,1), locate(0,0,B), locate(0,10.8,A), locate(10,0,C),
locate(-1,5,10), locate(5,0,10)


 )}}}

So we use the Pythagorean theorm:

AC² = AB² + BC²
AC² = 10² + 10²
AC² = 100 + 100
AC² = 200
 AC = <font face="symbol">Ö</font><span style="text-decoration: overline">200</span>
 AC = <font face="symbol">Ö</font><span style="text-decoration: overline">100·2</span>

 AC = 10<font face="symbol">Ö</font><span style="text-decoration: overline">2</span>

But if the triangle is labeled like this:

{{{drawing(200,200,-1,11,-1,11,triangle(0,0,0,10,10,0),
rectangle(0,0,1,1), locate(0,0,A), locate(0,10.8,C), locate(10,0,B),
locate(5,0,10) 


 )}}} then AC is also 10 feet {{{drawing(200,200,-1,11,-1,11,triangle(0,0,0,10,10,0),
rectangle(0,0,1,1), locate(0,0,A), locate(0,10.8,C), locate(10,0,B),
locate(-1,5,10), locate(5,0,10) )}}}

Then the answer is 10 feet and you don't need the Pythagorean theorm,
only the knowledge that isosceles triangles have two sides of equal
length. 

Edwin</pre>