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# Is ΔABC an isosceles triangle? (1) AD = DC (2) The area of ΔABD equal

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Math Expert
Joined: 02 Sep 2009
Posts: 56266
Is ΔABC an isosceles triangle? (1) AD = DC (2) The area of ΔABD equal  [#permalink]

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07 Aug 2018, 05:34
00:00

Difficulty:

45% (medium)

Question Stats:

51% (00:55) correct 49% (01:09) wrong based on 75 sessions

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Is ΔABC an isosceles triangle?

(2) The area of ΔABD equals the area of ΔBDC

Attachment:

GMAT_DS_Magoosh_168.png [ 4.16 KiB | Viewed 671 times ]

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Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: Is ΔABC an isosceles triangle? (1) AD = DC (2) The area of ΔABD equal  [#permalink]

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07 Aug 2018, 06:14
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Bunuel wrote:

Is ΔABC an isosceles triangle?

(2) The area of ΔABD equals the area of ΔBDC

Attachment:
GMAT_DS_Magoosh_168.png

So in ∆ABD and ∆BDC,
b) angles ADB = angle BDC=90
c) BD is common

So both triangles are similar and congruent, and hence sides AB=BC
Thus isosceles triangle
Sufficient

2) areas same
Height is same , so base is same or AD=DC
Same as above
Sufficient

D
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Re: Is ΔABC an isosceles triangle? (1) AD = DC (2) The area of ΔABD equal   [#permalink] 07 Aug 2018, 06:14
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