Complete the following proof.

given: abcd is rhombus
prove:

statement reason
1. 1. given
2. ad = bc = cd = ba 2.
3. do = ob; ao = oc 3. diagonals of a parallelogram bisect each other.
4. doa ≅ boa 4.
5. 5.
complete the two-column proof by providing the missing statements or reasons above.

Statment 2 is the definition of the rhombus: all the three sides have equal length. 
Statment 4 triangle DOA similar to BOA by the SSS statement of similar triangles (AD=AB, proven from statement 1, AO is side of both triangles, BO=OD from statement 3). 
Statment 5: angle 1 equals angle 2 from statement 4 since they are corresponding angles of the two triangles DOA and BOA.  

Reason for Statement 2: Definition of a rhombus (all sides congruent).

AD, BC, CD and BA are all the sides of the figure.  Since it is a rhombus, they will all be congruent.

Reason for Statement 3: Diagonals of a rhombus are perpendicular to each other.

These two angles form a linear pair; their sum is 180.  Since they are congruent, this means the measure of each is 180/2=90.  This is because the diagonals of a rhombus are perpendicular to each other.

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