Is MNO a right triangle?


(1) \(MN = 2\sqrt{2}\)

(2) ∠MNO = ∠MON = 1/2*∠OMN



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(1) mn = 2 ROOT 2. We can draw two such triangles with MN = 2root 2. Suppose MO=ON = 2root2, then we have a equilateral triangle with all angles = 60 degrees and the answer is NO Suppose OM=ON = 2, then we have a 45-45-90 degree right triangle and the answer is YES

Since we get a Yes and a No given the constraint, we mark NS

(2) <MNO = <MON = 1/2 OMN. Let MNO = MON = x, and OMN = x/2, then we have 2 1/2 x = 180. Solving gives 5/2 x =180 and x =72. Thus we have a 72-72-36 degree triangle, which is certainly not a right triangle, giving us a clear NO Sufficient.

The answer is B

The question asks whether triangle MNO is a right triangle, not whether angle MNO is a right angle. MNO could be right-angled if any of the three angles is right, not only angle MNO. So, here if you get from (2) that M = 90 degrees, then you still have an YES answer to the question: YES, triangle MNO is a right triangle.

Even if the question were "is angle MNO a right angle" and from one of the statement you get that angle NMO is right, then the statement is still sufficient because you got a definite NO to the question: NO, angle MNO is NOT a right angle (NMO is).
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