GMATPrepNow wrote:
Is CB || ED?
(1) ∆ABC and ∆AED are both isosceles triangles
(2) ∠C = ∠E
*kudos for all correct solutions
This question asks us to check the parallel line & it's transversal.
Here, BC & ED are the lines to be checked for parallelism and CD & BE are the transversals.
BC|| ED when the alternate angles in the given figure are equal. i.e, \(\angle{CBA}\)=\(\angle{AED}\) and \(\angle{ACB}\)=\(\angle{ADE}\)
Question stem: BC || ED? (Y/N)
Statement1:-∆ABC and ∆AED are both isosceles triangles
we only know that vertically opposite angles are equal, i.e, \(\angle{CAB}\)=\(\angle{EAD}\) and we don't know their measure in degrees.-----------(a)
Remaining two angles of both the isosceles triangles can have 'n' no of possible combinations.
hence st1 is not sufficient.
Statement1:-∠C = ∠E --------(b)
In ∆ABC and ∆AED, from (a) and (b) ,we have \(\angle{CBA}\)=\(\angle{ADE}\)
So, we can't say whether \(\angle{CBA}\)=\(\angle{AED}\) and \(\angle{ACB}\)=\(\angle{ADE}\) or not.
Hence statement2 is not sufficient.
(1)+(2), we have
(i) ∠C = ∠E
(ii)\(\angle{CAB}\)=\(\angle{EAD}\)
(iii) \(\angle{CBA}\)=\(\angle{ADE}\)
(iv) Both the triangles are isosceles; it has 2 cases:-
1.when \(\angle{E}\)=\(\angle{D}\)
then \(\angle{C}=\angle{D}\) & \(\angle{B}=\angle{E}\)
So, Is BC || ED? Yes (As alternate angles are found equal)
2.when \(\angle{E}=\angle{A}\)
then \(\angle{C}\neq\angle{D}\) & \(\angle{B}\neq\angle{E}\)
So, Is BC || ED? No (As alternate angles are not equal)
Ans. E