In the above quadrilateral ABCD, AD || EF || BC and
|AE| = 2 EB, BM = 4, |AD = 6, BC| =
, 9
Then DO

The length of segment is .

Step-by-step explanation:

Start by verifying that , and that .

Both and contain the angle . Hence, another pair of equal angles will be sufficient to prove by the angle-angle similarity postulate.

Notice that because , the corresponding angles next to those two lines would be equal: . Both is in whereas is in .

Hence, by the angle-angle similarity postulate.

Notice how in and in are two vertically opposite angles (and are thus equal to one another.) That is: .

Because , the alternate interior angles and are also equal to one another. That is:

Hence, , also by the angle-angle similarity postulate.

Notice that implies that:.

Therefore:

.

Similarly, implies that:

.

Therefore, .

.

It was already found that . Therefore:

.

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step-by-step explanation: