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3 Triangles

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by smclean23 » Wed Jul 30, 2008 4:13 pm
In the figure above, if PQRS is a square and QT = TR, which of the following statements is NOT true?
(A) PT = TS
(B) x = y
(C) u = v
(D) r = y
(E) The area of ΔPQT is equal to the area of ΔSRT.





Answer is D
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by Vignesh.4384 » Wed Jul 30, 2008 8:20 pm
IMO D.
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by smclean23 » Thu Jul 31, 2008 9:04 am
How did you come up with that answer? Whats the methodology?
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by pepeprepa » Thu Jul 31, 2008 9:13 am
First, I don't see it is a square.
Second, I don't know if T is at the middle of QR

So I am not sure with A,B,C,E
But I am sure r=y is wrong because r=v. Read the review of OG and list it, it is a really basic rule.

Tell me if I am wrong with that and if you know this kind of logic is common in the gmat.
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by sudhir3127 » Thu Jul 31, 2008 9:17 am
IMO D
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by VP_RedSoxFan » Thu Jul 31, 2008 9:28 am
I think the answer is D as well.

r = v because they are interior angles created when two parallel lines are cut by another line. pepeprepa is right about that, it is a standard geometry rule you'll need on exam day.

Therefore, for r = y, then y = v. If the whole thing is a square y = v when they are both 45 degrees which would only happen when the line that cuts them comes exactly from the other corner (this would create 2 45-45-90 triangles).

Since the cutting line comes from somewhere else, T, then y specifically does not equal v therefore making r never equal to y.

Ans = [D] Hope that helps.
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by dhanda.arun » Thu Jul 31, 2008 12:36 pm
The Answer is D.
Because
The triangles PQT and SRT are congruent (because of ASA condition)
So all other options are true except D.
:D
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Answer is D

by Gaurav Tyagi » Thu Jul 31, 2008 5:32 pm
It clearly says that QT=TR.
So, TR=1/2 QR.
For, r=v
TR should be equal to RS.
But as it is a square, RS = TR = 1/2 QR.

So, r cannot be equal to v.
Thanks,

GT
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proving congruent

by earth@work » Thu Sep 18, 2008 12:57 pm
method is to identify triangle(PQT) and (TRS) as congruent (QT=RS, angQ=angR=90', QT=TR therefore SAS rule applies) this will automatically give us answer D.
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by stop@800 » Thu Sep 18, 2008 10:56 pm
for r to be equal to y
TR has to be equal to RS

which is not the case
TR is RS/2
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