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

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

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New post 07 Aug 2018, 05:34
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

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

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Math Expert
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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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New post 07 Aug 2018, 06:14
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Bunuel wrote:
Image
Is ΔABC an isosceles triangle?


(1) AD = DC

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


Attachment:
GMAT_DS_Magoosh_168.png



1) AD=DC
So in ∆ABD and ∆BDC,
a) AD=DC
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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Is ΔABC an isosceles triangle? (1) AD = DC (2) The area of ΔABD equal

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