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

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) (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

RELATED QUESTIONS
Prove the following theorem: If the diagonals of a convex quadrilateral are... (answered by jim_thompson5910)

a) Prove the diagonals of a cyclic quadrilateral bisect each other b) prove if the... (answered by richard1234)

If the diagonals of a parallelogram are perpendicular, then the parallelogram must be a... (answered by TimothyLamb)

Please help me with the following proof. Thank you! How to prove statement "If a... (answered by KMST)

Answer each of the following T (true) or F (false). If FALSE, provide a counterexample (a (answered by Jalisa.)

Can you please help me with the following problem <<<<< write a paragraph proof for... (answered by Mathtut)

Math 9 theorem 3: the diagonals of a rhombus is perpendicular Proof!! Plss help me to... (answered by MathLover1)

Give a formal proof of the following theorem 1. A quadrilateral with one pair of... (answered by CPhill)