SOLUTION: Write the proof of the following theorem: if a quadrilateral is a kite, then its diagonals are perpendicular.

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Question 555730: Write the proof of the following theorem: if a quadrilateral is a kite,
then its diagonals are perpendicular.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
write the proof of the following theorem: if a quadrilateral is a kite,then its diagonals are perpendicular:
 
Given:  Kite ABCD
To prove: AC ⊥ BD
 
  

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


 1. AB ≅ AD
 2. BC ≅ CD
 3. AC ≅ AC 
 4. ᐃABC ≅ ᐃADC            4. SSS  (using 1,2, and 3)
 5. ∠BAE ≅ ∠DAE
 6. ᐃABD is isosceles
 7. ∠ABE ≅ ∠ADE
 8. ᐃABE ≅ ᐃADE            5. ASA  (Using 5,1, and 7)  
 9. ∠AEB ≅ ∠AED
10. ∠AEB ≅ ∠AED
11. m∠AEB = m∠ADE = 90°
12. AE ⊥ BD
13. AC ⊥ BD   
 
Edwin