Is AD the bisector of angle A in triangle ABC?

I am sorry the data makes complete sense.
Using both we can determine that AD is not an angular bisector.It stands out just as median.

Yes. A median can be angular bisector if it is an altitude.

thanks nightfury. very helpful!

Below cases can be possible and can be useful in exam.

1) Median ,Angle bisector and perpendicular will be same if triangle is isosceles or equilateral triangle. Opposite is also true for this.
2) Median can be angle bisector only if it is perpendicular as well and this applies vice-versa like angle bisector can be median if it is perpendicular also.

Answer of this would be C as we can figure out that AD is not abgle bisector.

I could not understand the problem, can somebody help me understand this

Thanks sandal85. Indeed useful corollaries to remember.

Harsha, this is a problem in geometry in which you have a triangle abc. A line AD is made that intersects the line BC at point D. We are asked if this line AD is an angle bisector of angle A.
1. says that the area of are of the two triangles now formed (becuase of line AD) are equal
2. says that this line AD is perpendicular to side BC

does it make sense now?

Thanks Sansal85... these tips really help... keep posting

Why is anyone assuming that point D is on BC?
If it is a point somewhere else, AD may/may not be the median.

Please explain.

cyberjadugar, you are right. It cannot be assumed that D is on line BC unless explicitly stated in some way. However, i this I assume is not the result of poor question framing more than anything! on the GMAT it would be explicitly stated that D is on BC.

However, cyberjadugar, IMO even if we assume that D is not a point on BC the result doesnt change much. Both the statements still continue to provide the same amount of information.

Ideally, the GMAC would surely make sure to mention that D is a point on BC. However, the question is a good one as a number of times we make a mistake of not choosing a possibility that 'NO' can also be an answer in DS.

Regards,

Shouvik.

But won't AD only be bisector of angle A if D is the height on segment BC hence perpendicular? Could someone please explain this one?


I think what’s going on here.

Statement 1 we have that the areas of both triangles created by line AE have same areas. Well, we still don't know if this is the bisector of angle A. Put it this way, we could have that BC>AC, and thus compensating for the area, AD needs not to be the bisector of A. In other words, it will ONLY be the bisector of A is AD is perpendicular to BC, which we can't assume from this information

Statement 2 tells us that AD is NOT perpendicular to BC. We could have AD be the bisector of angle A (as in statement 1) if the triangle is constructed similarly. Likewise, we could have that AD stands somewhere else thus making the triangle have different areas. Clearly insufficient

Both together, we know that the areas are the same and that AD is NOT perpendicular to BC. Therefore, AD CANNOT be the bisector of angle A for the reasons explained above.

C stands

Thanks
Cheers
J

Calling Experts..

I don't think OA in this question is correct..

Assuming that D is a point on BC,

(1) Triangle ABD and triangle ACD have equal areas
Means that BD = CD

Because Area = \(\frac{1}{2}*Base *Height\)
Since, Height is Constant, Bases of both the triangles has to be equal. Hence, CD = BD.
Therefore, AD has to be the Angle Bisector Irrespective of it being Perpendicular to BC.

My Answer: A

Expert solution required. thanks

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