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.
<span>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.</span>
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