How do you verify that the diagonals of a rhombus bisect each other?

  • Thread starter Thread starter Brenda N
  • Start date Start date
Draw the rhombus ABCD, Draw the two diagonals AC and BD and label the intersection as E.

AB ≡ BC ≡ CD ≡ DA : Given. The sides of a rhombus are congruent.
AC ≡ AC ; Reflixivity
ΔACB ≡ ΔACD : SAS
m<EAB = m<ECD : CPCTC
m<EAB = m<ECB : In ΔACB, they are opposite equal sides
m<EAD = m<ECD : In ΔACD, they are opposite equal sides
m<EAB = m<EAD : Both equal to m<ECB
m<ECB = m<ECD : Both equal to m<EAB
BD ≡ BD ; Reflixivity
ΔABD ≡ ΔCBD : SAS
m<EBC = m<EDA : CPCTC
m<EBA = m<EDA : In ΔABD, they are opposite equal sides
m<EBC = m<EDC : In ΔCBD, they are opposite equal sides
m<EBA = m<EBC : Both equal to m<EDA
m<EDC = m<EBC : Both equal to m<EBC
ΔABE ≡ ΔBCE : ASA
ΔABE ≡ ΔCDE : ASA
ΔCDE ≡ ΔDAE : ASA
ΔDAE ≡ ΔABE : ASA
ΔABE ≡ ΔBCE ≡ ΔCDE ≡ ΔDAE : Transitivity
AE ≡ EC : CPCTC ΔABE ≡ ΔCDE
BE ≡ ED : CPCTC ΔABE ≡ ΔCDE
QED
 
This should help:

http://www.algebra.com/algebra/homework/Parallelograms/prove-that-the-diagonals-of-parallelogram-bisect-each-other-.lesson

http://en.wikipedia.org/wiki/Parallelogram#Proof_that_diagonals_bisect_each_other
 
this question was on my york university prerequisite test. u wouldnt happen to b studying for the same one would you???
 
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