#10.
If the two triangles are similar, then their sides are proportional.
EC we know immediately. If the whole side BC = 12 = BE + EC, and BE is 4, then EC = 8.
Therefore, I can say that BD / (BD + DA) = BE / (BE + EC). To solve the problem for side DA, x will be used in place of DA.
8 / (8 + x) = 4 / (4 + 8)
8 / (8 + x) = 4 / 12 || Cross-multiply
4(8 + x) = 12 * 8
32 + 4x = 96
4x = 64
x = 16
AD = 16
Then, if we know AD, we can easily find AB. AB = AD + DB. AB = 24.
Lastly, we need to find AC. All of the other lengths on the big triangle have been double that of the smaller triangle, so 6 x 2 = 12. AC = 12.
#11.
BC will be parallel to DE if the proportions are equal.
AE / AB = AD / AC
1 / 5 = 2 / 11
These fractions are not equivalent, therefore BC and DE are not parallel.
Hope this helps!! :)