Question

Could someone help me out please!

Answer 1

Answer:

1. BC = 6
2. x = 5
3. CE = 16
4. Yes, BC║DE

Step-by-step 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.