Diagonal AC divides quadrilateral ABCD into two triangles. Are these triangles congruent?
(1) AD||BC
(2) AB=CD
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triangles congruent?
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patanjali.purpose
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neelgandham
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Diagonal AC divides quadrilateral ABCD into two triangles. Are these triangles congruent?
ABCD can be a Paralellogram (Where the triangles are congruent) or
ABCD can be a Trapezoid (Where the triangles are non-congruent)
Hence Insufficient!
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
Then(1) AD||BC
ABCD can be a Paralellogram (Where the triangles are congruent) or
ABCD can be a Trapezoid (Where the triangles are non-congruent)
Hence Insufficient!
then(2) AB=CD
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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Anil Gandham
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Hi Neelgandham,neelgandham wrote: From one and two again(see attachment), ABCD can be an Isosceles Trapezoid
Don't the diagonals of an Isosceles Trapezoid divide Trapezoid equally? I think they do.
Thanks!
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LalaB
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@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
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
