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Is quadrilateral RSTV a rectangle?

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Is quadrilateral RSTV a rectangle? [#permalink] New post 19 Apr 2012, 12:15
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Is quadrilateral RSTV a rectangle?

(1) The measure of ∠RST is 90o
(2) The measure of ∠TVR is 90o
[Reveal] Spoiler: OA

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Last edited by Bunuel on 19 Apr 2012, 12:25, edited 1 time in total.
Added the OA
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Re: Is quadrilateral RSTV a rectangle? [#permalink] New post 19 Apr 2012, 12:27
Expert's post
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
Kite.png [ 4.09 KiB | Viewed 2204 times ]

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Re: Is quadrilateral RSTV a rectangle? [#permalink] New post 20 Apr 2012, 19:26
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] New post 21 Apr 2012, 02:08
yeah right missed this figure :):) Thanks
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Re: Is quadrilateral RSTV a rectangle? [#permalink] New post 05 Aug 2013, 19:22
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] New post 05 Aug 2013, 21:04
madn800 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)
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Re: Is quadrilateral RSTV a rectangle? [#permalink] New post 05 Aug 2013, 22:12
Asifpirlo wrote:
madn800 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] New post 27 Mar 2014, 07:04
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] New post 27 Mar 2014, 07:38
Expert's post
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
Untitled.png [ 5.18 KiB | Viewed 580 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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Is quadrilateral RSTV a rectangle?   [#permalink] 27 Mar 2014, 07:38
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