3 Triangles

[smclean23]

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

[Vignesh.4384]

IMO D.

[smclean23]

How did you come up with that answer? Whats the methodology?

[pepeprepa]

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.

[sudhir3127]

IMO D

[VP_RedSoxFan]

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.

[dhanda.arun]

The Answer is D.
Because
The triangles PQT and SRT are congruent (because of ASA condition)
So all other options are true except D.

[Gaurav Tyagi]

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.

[earth@work]

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.

[stop@800]

for r to be equal to y
TR has to be equal to RS

which is not the case
TR is RS/2