Is quadrilateral ABCD a rectangle?
(1) Line segments AC and BD bisect one another.

(2) Angle ABC is a right angle.


OA is C.

From 2) I can see that its either square or rectangle so cross off b and d
From 1) I can still only see its a square

I can't tell why C tells me its rectangle but not a square? When the lines bisect each other, doesn't it create 45 degree angles, thus 45-45-90, making all sides x radical 2? THus, its a square? Please advise!

When diagonals bisect, they are not necessarily perpendicular bisectors of each other. For a rectangle to be a square, the diagonals have to be perpendicular bisectors, not just bisectors.

So just to follow up.

Is the Answer C or E?

If C, givemeanid, or someone else - can you please explain in further detail?

Thanks!

1. When diagonals bisect each other, the quadrilateral is a parallelogram. However, this is not enough to say that the quad is a rectangle.
INSUFFICIENT.

2. Angle ABC = 90 degrees does not mean the quad is rectangle. We do not know anything else.
INSUFFICIENT.

Now, combining together, we know it is a parallelogram with one angle = 90 degrees. This is sufficient to say that the quad is a rectangle. (To figure this, since one angle is 90, the opposite angle is 90 too. In a parallelogram, opposite angles are equal. So, we have a pair of angles, each = 90. Since the sum of all 4 angles = 360, sum of the other pair = 360 - 90*2 = 180. Since, these angle are also equal to each other, they are also 90 degrees each. So, all angles are 90 degrees and diagonals bisect. The quad is a rectangle.)
SUFFICIENT.

Answer is C.

Is it true that all squares are also rectangles?

Yes. All squares are rectangles. However, the inverse is not true.

Nice, givemeanid. Keep up the great work!