Question 555730
write the proof of the following theorem: if a quadrilateral is a kite,then its diagonals are perpendicular:
<pre> 
Given:  Kite ABCD
To prove: AC &#8869; BD
 
{{{drawing(250,500,-4.5,4.5,-6.5,5.5, locate(0.2,-.1,E),
locate(0,5.5,A), locate(-4.3,0,B), locate(0,-6,C), locate(4,0,D),
line(-4,0,0,5), line(0,5,4,0),line(4,0,0,-6), line(0,-6,-4,0),
green(line(-4,0,4,0),line(0,5,0,-6))  )}}}  

A couple of reasons are filled in.  You fill in the rest:


 1. AB &#8773; AD
 2. BC &#8773; CD
 3. AC &#8773; AC 
 4. &#5123;ABC &#8773; &#5123;ADC            4. SSS  (using 1,2, and 3)
 5. &#8736;BAE &#8773; &#8736;DAE
 6. &#5123;ABD is isosceles
 7. &#8736;ABE &#8773; &#8736;ADE
 8. &#5123;ABE &#8773; &#5123;ADE            5. ASA  (Using 5,1, and 7)  
 9. &#8736;AEB &#8773; &#8736;AED
10. &#8736;AEB &#8773; &#8736;AED
11. m&#8736;AEB = m&#8736;ADE = 90°
12. AE &#8869; BD
13. AC &#8869; BD   
 
Edwin</pre>