Answer:
- BC = 6
- x = 5
- CE = 16
- Yes, BC║DE
Explanation:
1. The parallel lines make the various triangles similar, so the corresponding sides are in proportion.
... BC/AB = FE/A.F
... BC/9 = 4/6
... BC = 9·4/6 = 6
2. As in problem 1, the triangles are similar, so ...
... x/(x+10) = 10/30
... 30x = 10x + 100 . . . . multiply by 30(x+10)
... 20x = 100 . . . . . . . . . subtract 10x
... x = 100/20 = 5
3. As in problems 1 and 2, the triangles are similar, so ...
... AD/DB = CE/EB
... 24/27 = CE/18
... 18·24/27 = CE = 16
4. If the lines of interest are parallel, the triangles will be similar and corresponding measures will be in proportion.
Compare AD/DB = 15/12 = 5/4 to AE/EC = 10/8 = 5/4. These are equal, so corresponding measures are proportional. Therefore we conclude the triangles are similar and BC║DE.