Question

Hey, can anyone help me solve these? I just need a little push.

Answer 1

Are there answer choices?

@Wolfadaskies

Answer 2

nvm i can't seem to get it i understand the question just not how to explain

Answer 3

Nope, no answer choices I'm afraid.. @AihberKhan

Answer 4

you can use Thales theorem

Answer 5

you know of it?

Answer 6

if XY||DF
\[\frac{EX}{XD}=\frac{EY}{YD}=\frac{8}{DF}\]

Answer 7

we know that EY is congruent to YD
EY=YD
therefore: \[1=\frac{8}{DF}\]

Answer 8

finish the work

Answer 9

oh mistake i forgot how this theorem works, after checking online
it should be \[\frac{EX}{ED}=\frac{EY}{EF}=\frac{8}{DF}\]
\[ED=2EX \Longrightarrow \frac{1}{2}=\frac{8}{DF} \Longrightarrow DF=16\]

Answer 10

\[\color {red} {\text {the theorem is called: "Thales's intercept theorem"}}\]

Answer 11

https://en.wikipedia.org/wiki/Intercept_theorem

Answer 12

This bring good memories to me lol
i haven't seen this theorem in awhile

Answer 13

Ah Hell, my computer was frozen. I read back through this and I'm understanding it a lot better now, thank you so much! @xapproachesinfinity