## Sunshine447 2 years ago Look at the figure shown below.

1. Sunshine447
2. Sunshine447

Which statement must be true to prove that segment DE is parallel to segment CA?

3. Sunshine447

4 : EA = 1 : DC 2 : DC = 5 : EA 3 : EA = 2 : DC 1 : DC = 2 : EA

4. Sunshine447

@phi hopefully this will be the last question I need help with...

5. phi

6. Sunshine447

7. Sunshine447

now can you?

8. phi

if DE is || to CA then the sides of the triangle are transversals |dw:1359074409155:dw| if the lines are parallel then the marked angles are equal "corresponding angles" of a transversal if the angles are all the same, the top little triangle is similar to the big triangle. that means you want the sides to be in proportion

9. Sunshine447

okay,but how do we make the sides proportionate?

10. Sunshine447

@phi ?

11. phi

for example you can say the legs of the little triangle on top are in the ratio of 16/24 or simply 2/3 the legs of the big triangle are in the same ratio BC/BA but that isn't in any of the choices also, the segments, DC/EA are in proportion $\frac{2}{3} = \frac{DC}{EA}$ that looks promising but it's not in the same form as your choices we can reorder things, by first cross multiplying 2*EA = 3*DC now divide by EA : 2= DC * 3/EA divide by DC 2/DC = 3/EA

12. phi

you can write 2/DC = 3/EA this way 2: DC = 3:EA or 3 : EA = 2 :DC

13. Sunshine447

okay! so it's C?

14. phi

yes.

15. Sunshine447

Oh my gosh @phi , I have no clue how, but you make it possible for me to understand math! Thanks sooooo much for ALL the help you've given me! :)

16. phi

yw