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# Is quadrilateral RSTV a rectangle?

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Updated on: 09 Jan 2019, 02:10
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Is quadrilateral RSTV a rectangle?

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

Originally posted by shikhar on 19 Apr 2012, 13:15.
Last edited by Bunuel on 09 Jan 2019, 02:10, edited 2 times in total.
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Re: Is quadrilateral RSTV a rectangle?  [#permalink]

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19 Apr 2012, 13:27
5
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shikhar wrote:
Is quadrilateral RSTV a rectangle?

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

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

Kite.png [ 4.09 KiB | Viewed 8539 times ]

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Re: Is quadrilateral RSTV a rectangle?  [#permalink]

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27 Mar 2014, 08:38
2
dangeyg wrote:
Bunuel wrote:
shikhar wrote:
Is quadrilateral RSTV a rectangle?

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

It's clear E. Sure RSTV can be a rectangle but it also can be a kite:
Attachment:
The attachment Kite.png is no longer available

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.

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:
Attachment:

Untitled.png [ 5.18 KiB | Viewed 6888 times ]
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.
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Re: Is quadrilateral RSTV a rectangle?  [#permalink]

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25 Sep 2019, 01:04
2
For rectangle :

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

dcummins wrote:
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.

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Re: Is quadrilateral RSTV a rectangle?  [#permalink]

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20 Apr 2012, 20:26
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Nice got it right, went with E since both stems give the opposite angles and not the adjacent angles, it can be a diamond.
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Re: Is quadrilateral RSTV a rectangle?  [#permalink]

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05 Aug 2013, 23:12
1
Asifpirlo wrote:
The figure can be a square too. We cannot say unless we have info about the length of sides.
straight E.

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

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.
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Re: Is quadrilateral RSTV a rectangle?  [#permalink]

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21 Apr 2012, 03:08
yeah right missed this figure :) Thanks
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Re: Is quadrilateral RSTV a rectangle?  [#permalink]

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05 Aug 2013, 20:22
The figure can be a square too. We cannot say unless we have info about the length of sides.
straight E.
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Re: Is quadrilateral RSTV a rectangle?  [#permalink]

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05 Aug 2013, 22:04
The figure can be a square too. We cannot say unless we have info about the length of sides.
straight E.

RSTV can be a square or rectangle. so double case. Answer (E)
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Re: Is quadrilateral RSTV a rectangle?  [#permalink]

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27 Mar 2014, 08:04
Bunuel wrote:
shikhar wrote:
Is quadrilateral RSTV a rectangle?

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

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

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.
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Re: Is quadrilateral RSTV a rectangle?  [#permalink]

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14 Mar 2017, 17:39
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.
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Re: Is quadrilateral RSTV a rectangle?  [#permalink]

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07 Jan 2019, 07:04

Project DS Butler: Day 63: Data Sufficiency (DS125)

Bumping for DS butler Projec
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Re: Is quadrilateral RSTV a rectangle?  [#permalink]

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25 Sep 2019, 00:35
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.
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Re: Is quadrilateral RSTV a rectangle?   [#permalink] 25 Sep 2019, 00:35
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