In the below diagram, BC is parallel to DE. Given AC:CE=2:3, express #vecDE# in term of #vecBC#?
If BC is parallel to DE, then the triangles are similar, which means that all sides are proportional.
We are given that AC:CE = 2:3
So, the ratio of AC to the comparable side of the larger triangle, which is AE = AC + CE is:
So, they are similar triangles, so BC/DE is the same ratio:
...you can cross multiply:
...and then you can write an equation for DE in terms of BC: