Is quadrilateral RSTV a rectangle?

Question

(1) The measure of ∠RST is 90o
(2) The measure of ∠TVR is 90o

Bunuel · Answer

It's clear E. Sure RSTV can be a rectangle but it also can be a kite: Kite.png

aalba005 · Answer

Nice got it right, went with E since both stems give the opposite angles and not the adjacent angles, it can be a diamond.

shikhar · Answer

yeah right missed this figure

:) Thanks

madn800 · Answer

The figure can be a square too. We cannot say unless we have info about the length of sides.
straight E.

Asifpirlo · Answer

RSTV can be a square or rectangle. so double case. Answer (E)

Dmitriy · Answer

Square is a kind of rectangle, which has equal sides. Therefore, it is not double csse.

The reason why E is the answer is that we can draw figures with angles different from 90º.

dangeyg · Answer

Can you provide some more explanation here.
1. Straight lines never bends...even at infinity. 
2. In your kite example angle at S and V is 90, but then line started bending inwards, making it a kite.
3. Mathematically lines originating from angle S and V will travel straight and intersect other lines perpendicularly. i.e Only applicable when opposite ends are at 90.

Real life example, open MS Paint and see how we draw rectangles in it. You click at one end and drag cursor diagonally. one can see opposite ends at right angle.

Bunuel · Answer

Frankly I don't see the lines bending inwards in the figure. Anyway, are you implying that such figure is not possible? If yes, then you are wrong: Untitled.png The angles marked as right must be right because if an inscribed triangle has diameter as its hypotenuse then the triangle must be right angled. So, we can inscribe a right triangle in a circle and then draw its mirror image around the hypotenuse to get a kite. Hope it's clear.

Nunuboy1994 · Answer

Is quadrilateral RSTV a rectangle?

(1) The measure of ∠RST is 90o
(2) The measure of ∠TVR is 90o

In order to solve this question we need to see if we can derive any properties of a rectangle from either each statement or both.

Statement (1) tells us that the measure of ∠RST is 90o- this is perhaps enough information to tell us that the shape is a rhombus but the shape, as stated, could be a diamond. Insufficient.

Statement (2) tells us that ∠TVR is 90o- though this statement only gives us as much information as Statement (1) and is therefore inconclusive. Insufficient.

Both statements taken together could imply a rectangle, though again they could imply a diamond.

dcummins · Answer

Okay so what do we need here to know if its a rectangle?
- all angles?
- 2 sides?

Rectangle = opposite sides are equal, thus opposite angles are equal.

GMATBusters · Answer

For rectangle :

Quadrilateral

1) all angles equal to 90.
Or
2) parallelogram with diagonals equal.

Posted from my mobile device

coreyander · Answer

Even with adjaced angles at 90 degree, the quadrilateral need not be a rectange.

altairahmad · Answer

With just 2 adjacent right angles the shape can be e.g a right trapezoid but with three right angles it has to be a square/rectangle. Right ?

coreyander · Answer

Sum of interior angles of Quadrilateral = 360- 3*90 = 90..

When three angles are 90, the fourth will be 90.. It should be a rectangle/square.

Shane04 · Answer

Can any of the experts please clarify this<

Since we haven't been given info about the sides of the quadrilateral, RSTV can also be a square right?
Or does the logic that all squares are essentially a type of rectangle, a reason we are not considering it and instead the kite is the only reason for E?

Bunuel

Bunuel · Answer

Yes, we've already established that RSTV could be a rectangle. And since all squares are rectangles, it implies that RSTV could also be a square.

bumpbot · Answer

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Is quadrilateral RSTV a rectangle?

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