## Sunshine447 Group Title Look at the figure shown below. one year ago one year ago

1. Sunshine447 Group Title
2. Sunshine447 Group Title

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

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

4. Sunshine447 Group Title

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

5. phi Group Title

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7. Sunshine447 Group Title

now can you?

8. phi Group Title

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 Group Title

okay,but how do we make the sides proportionate?

10. Sunshine447 Group Title

@phi ?

11. phi Group Title

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 Group Title

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

13. Sunshine447 Group Title

okay! so it's C?

14. phi Group Title

yes.

15. Sunshine447 Group Title

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 Group Title

yw