pappueshwar wrote:In the figure shown, if the measure of angle BAD is 60 degrees, ABCD is a parallelogram, and line BC bisects line AE, what is the length of side EC?
(1) The length of DC is 12.
(2) The length of BC is 12.
OA IS C. Please assist in solving
In DS, we don't really need to solve till end as soon as we realize that the term in question can be uniquely determined from here on. We can use facts as those are to cut it short. The useful fact is
A triangle can be completely determined when two of its sides and their included angle are known.
Let's see what do we have in order to find the length of side EC in ∆EBC, before reading any statement?
If the measure of ∠BAD is 60°, then the measure of ∠EBC is also 60°, as ABCD is a parallelogram and these are corresponding angles. (see Parallel Lines)
If line BC bisects line AE, then BE = AB = DC.
Coming back to the question...
In ∆EBC, we have ∠EBC = 60° and we want to find the length of side EC. Hence, we must know the length of both including sides EB (= AB = DC) and BC.
I. If the length of DC is 12, then EB = 12, and we don't know the length of BC. Insufficient
II. If the length of BC is 12, then we don't know the length of EB. Insufficient
When two statements are taken together, we then have
In ∆EBC, EB = 12, BC = 12, and the included ∠EBC = 60°
[spoiler]
Sufficient material to determine the length of side EC, uniquely
Hence C[/spoiler]
