In the figure above, D is a point on the side AC of ABC.Is ABC isos?

Question

https://gmatclub.com/forum/download/file.php?id=25004 In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosceles? (1) The area of triangular region ABD is equal to the area of triangular region DBC. (2) BD┴AC and AD = DC triang ABCD.JPG

kinghyts · Answer

Statement 1: The area of triangular region ABD is equal to the area of triangular region DBC.

This means that the point D is mid-point of AC. But, we can't still say whether the triangle ABC is isosceles or not. Insufficient.

Statement 2: BD┴AC and AD = DC. Signifies that the median drawn from the vertex B is a perpendicular bisector. This can only happen if the triangle is isosceles triangle with AB = BC. Sufficient

The answer should be B

JJo · Answer

In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosceles?

(1) The area of triangular region ABD is equal to the area of triangular region DBC --> this gives us info that D is the midpoint of AC but we don't have any info about angle ADB & BDC....insufficient
(2) BD┴AC and AD = DC --> this gives us info that D is midpoint of AC and that BD┴AC, this condition will make AB=BC.......sufficient.(refer below image, hope my understanding is correct

)

Ans. B)

Attachments

File comment: triangle

triangle.png [ 7.79 KiB | Viewed 24591 times ]

) Ans. B)

noTh1ng · Answer

What exactly does this "BD┴AC" say?

I don't know what the symbol means.

Bunuel · Answer

It means that BD is  perpendicular  to AC.

ENGRTOMBA2018 · Answer

Per statement 1, Area Triangle (BAD} = Area Triangle {BDC}

---> 0.5*BE*AD = 0.5*BE*CD ---> AD = CD . But no information about AB and BC. Thus this triangle may or may not be isosceles. Thus this statement is not sufficient.

Per statement 2, BD┴AC and AD = DC ---> Triangles BDA and BDC are congruent. ---> AB = BC ---> Triangle ABC is isosceles. Thus this statement is sufficient.

B is the correct answer.

ENGRTOMBA2018 · Answer

Statement 1 is straightforward to see that it is NOT sufficient. The most this statement will do is to provide a scenario when we have AD=CD. But this does not yet answer the question asked.

Statement 2, is tricky as in from the figure provided, BD can either be to the left of A or between A and C or to the right of C. But in only 1 case (of between A and C) will you get AD=CD such that BD  \perp  AC. With this scenario, triangle ABC is indeed isosceles (by making triangles ABD and BCD congruent to each other by the SAS property ---> AB=BC) . Hence sufficient.

B is the correct answer.

Hope this helps.

sydneygmat1 · Answer

Answer: B

We are after: Is ΔABC isosceles?

(1) Not sufficient. Using the formula for areas of triangle, we get

Area of ΔABD = Area of ΔABD
1/2 * AD * h = 1/2 * DC * h

h is the height for both triangles, if you drop a perpendicular from point B on AC. This will fall on the extended AC (if you can imagine it)

The above equation yields to: 
AD = AC

But we want to know if ΔABC is isosceles. This information doesn't help so it is INSUFFICIENT.

(2) Sufficient

Since BD ⊥AC, and D is on AC, imagine D dividing AC into two sides i.e. AD =AC.

Now imagine two right angled Δs inside ABC being split in the middle by BD. These two right angled Δs have the same base and height so the hypotenuse will be same i.e. AB = AC

Bishal123456789 · Answer

Bunuel   VeritasKarishma   chetan2u  Cant option B result in equilateral triangle?

chetan2u · Answer

Hi Bishal,

Yes, it CAN be an equilateral triangle....
Of course, it is an isosceles triangle for sure.. also all equilateral triangles are Isosceles

mrmba11 · Answer

A strong takeaway in this Q is that ALL equilateral triangles are ALSO isosceles triangle. If we forget this rule, we might reject option B.

The triangle property is ' When an perpendicular bisects the base into equal parts (AD=DC for example as per the Q), then such triangle (ABC) must be an isosceles or equilateral triangle.

gmatftw777 · Answer

Is this question still relevant for gmat FE?  Bunuel

Bunuel · Answer

______________________________
No. You can ignore it and move on.

In the figure above, D is a point on the side AC of ABC.Is ABC isos?

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