I will give it a try.

Knowing that DC is 12 that means AB is 12. And since BC bisects AE, AB is equal to BE. So BE is 12. However we cannot figure out the length of the other sides of the triangle or parallelogram.

Knowing BC is 12 we know AD is 12 however that doesn't help figuring out EC.

If you combine. You know the parallelogram is 12 on all sides. Therefore you are looking at a equilateral triangle. Because AE is bisected by BC angle ABC is 120 therefore EBC is equal to 60(str8 line - 120), EBC is equal 60 degrees and BE is 12 and BC is 12. So that means 180 - 60 = 120 and since the last two angles are equal 120/2 = 60. Therefore you know EC is equal to 12.

I hope that makes sense

Hope this pic helps explain it better...



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Wel... We can solve this by combining both the answer choices.

If the angle of BAD is 60, then it obviously means EBC is 60degrees, so for the traingle the total angle equals 180. So 180 - 60 =120. So remaining two sides 2x = 120 , x = 60.

1:If the line BC intersects AE, then AB = 12 so do Be. AB = BE = 12.So based on this we cannot find the solution.
2: If the length of BC = 12 , then we cannot find out the answer.

Combine both.

We got BE and BC and the and the angle B = 60 and all the angles are equal to 60. So apparently all the sides are equal to 60.

So, as we found out

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

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]