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The figure below shows a parallelogram ABCD with perpendicular diagonals AC and BD. If it is given that angle DAB is 80°, which statement is sufficient to guarantee that the parallelogram is a rhombus with all sides equal?

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Angle CAB is 40°, and angle DBA is 50°. Angle CAB is 50°, and angle DBA is 60°. Angle DBA is 40°. Angle CAB is 60°.
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@AccessDenied here it is ^^

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now when they say DAB is 80 degrees do they mean angle A or what?
|dw:1338659650776:dw| That entire angle.
ah k
I am thinking this deals with the idea that the diagonals should bisect their respective angles... so I believe we can assume this is true for it to be a rhombus: |dw:1338659975193:dw|
So, if we are bisecting an angle of 80 degrees, then we know that the bisected angle is 1/2 of 80, or 40: |dw:1338660097272:dw|
So, you can also conclude that the other angle using the sum of interior angles of a triangle. 40 + x + 90 = 180, x = 50 Now, which answer 'fits' for our diagram now? |dw:1338660264049:dw|
A :D
Yep! Basically, we just assume that it is a rhombus, and that the properties of a rhombus apply. The ideal answer should just pop out as we fill in the information. :D
Thank you very much. Four more to go. You up to it? :)
Yep. :P

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