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triangles congruent?

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Source: — Data Sufficiency |
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by neelgandham » Sun Jan 01, 2012 10:15 am
Diagonal AC divides quadrilateral ABCD into two triangles. Are these triangles congruent?
(1) AD||BC
Then
ABCD can be a Paralellogram (Where the triangles are congruent) or
ABCD can be a Trapezoid (Where the triangles are non-congruent)
Hence Insufficient!
(2) AB=CD
then
ABCD can be a Paralellogram (Where the triangles are congruent) or
ABCD can be some other quadrilateral (Where the triangles are non-congruent)
Hence Insufficient!

From one and two again(see attachment), ABCD can be an Isosceles Trapezoid
Hence Insufficient!

IMO E
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by apex231 » Mon Jan 02, 2012 8:29 am
neelgandham wrote: From one and two again(see attachment), ABCD can be an Isosceles Trapezoid
Hi Neelgandham,

Don't the diagonals of an Isosceles Trapezoid divide Trapezoid equally? I think they do.

Thanks!
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by LalaB » Mon Jan 02, 2012 8:41 am
@apex231 , hmm I have doubts ...

from the pic above we can see, that ADC and ABD are congruent. but not ADC and ACB. (u can be sure of it even visually) if u want to be sure from more practical view, then lets see-

ADC and ABD

AC=BD
AD is the same for ADC and ABD
AB=DC
so, ADC and ABD are congruent


now ADC and ACB-
AB=DC
Ac is the same for ADC and ACB
but Ad is not equal to BC.
so, DC and ACB are not congruent
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