Bunuel wrote:
kkrrsshh wrote:
Bunuel wrote:
getitdoneright wrote:
Having a very hard time understanding any of the explanations of why statement 2 is insufficient. The question seems to imply that angle ACD is 90 degrees. If AB = BC = BD, doesn't that mean that angle ACB + BCD = 90?
Yes, angle ACD is 90 degrees and ACB + BCD = 90 degrees but the point is that we don't know whether CB is perpendicular to AD. Not knowing that, how are you getting that (2) is sufficient?
Hi
Bunuel,
Its given,AB=BC=BD
So here, it satisfies this equation: BC^2=AB.BD
This implies, CB is perpendicular to AD.
Can you please tell whether this understanding is flawed?
Useful property: The median on the hypotenuse of a right triangle always equals to one-half the hypotenuse.AB = BC = BD means that CB is the median (B is the midpoint of AD). Because of the property above, AB = BC = BD is true for any right angled triangle with median CB. So, CB may or may not be perpendicular to AD.
Hi
Bunuel,
chetan2u,
VeritasKarishmaIn STMT 2,
It is provided that AB=BD=CB,
Which means that Angle CAB = Angle ACB = Angle BCD = Angle CDB = x.
So would it be incorrect to assume that the triangles ACB and CBD are congruent(Angle CAB = Angle CDB and Angle ACB = Angle BCD ) wih BC being the common side. For this to be possible Angle CBA needs to be a right angle and Angle CDB hence becomes 45
Even solving it geometrically,
We would be arriving at Angle CBA = 180 -2x(Angle sum property)
And Angle CBD to be 2x
In Triangle BCD, Angle CDB and Angle BCD are equal to x
so 4x =180
x= 45 and 180-2x =90
Consequently, I feel that the Answer should be D. Could you please point out where I am going wrong?
Thank You