http://i1042.photobucket.com/albums/b421/Leilani_Jeraffi/Mobile%20Uploads/image_zpsqbwzwlch.jpg

For , the following facts are given:

TE = 6 cm
OT = 2 cm
OE = 5.8 cm
OG = 4.35 cm
AU = 0.45 cm

Use this information to answer the following:
Why is ?
Now find the following missing lengths. Show all work or reasoning. Round non-integral lengths to the nearest hundredth.
a. GE
b. TS
c. OA
d. BT (Use the Side-Splitting Theorem)
e. SE
f. OU
Answer:

Question

http://i1042.photobucket.com/albums/b421/Leilani_Jeraffi/Mobile%20Uploads/image_zpsqbwzwlch.jpg 

For , the following facts are given: 

TE = 6 cm 
OT = 2 cm 
OE = 5.8 cm 
OG = 4.35 cm 
AU = 0.45 cm 

Use this information to answer the following: 
Why is ? 
Now find the following missing lengths. Show all work or reasoning. Round non-integral lengths to the nearest hundredth. 
a. GE 
b. TS 
c. OA 
d. BT (Use the Side-Splitting Theorem) 
e. SE 
f. OU 
Answer:

wolf1728 · Answer

This graphic should make it a LOT easier to solve this.

milalulu · Answer

i already have that graphic. im not exactly sure where or how to even start this problem

milalulu · Answer

it's the only one out of all my homework that I am absolutely clueless about.

directrix · Answer

In the question, what word is supposed to be between the "Why is" and the ? symbol?

>>Use this information to answer the following: Why is ?

wolf1728 · Answer

I figured I'd add a little more information to my graphic.

milalulu · Answer

Thank you!! @wolf1728

milalulu · Answer

that was an accident, you can ignore that! @directrix

directrix · Answer

Okay.

directrix · Answer

In Triangle OTE, seg BG is parallel to seg TE

That brings up the theorem:

If a line is parallel to one side of a triangle and intersects the other two sides of the triangle, then those sides are divided proportionally.

That gives:

OT is OB as OE is to OG

2/x = 5.8/4.35

Use the Means-Extremes Property to get that OB = 1.5

directrix · Answer

That adds two bits of information to the diagram.

directrix · Answer

Looking at Tri TOS, seg BN is parallel to seg TS.

Once again, this theorem is in play:

If a line is parallel to one side of a triangle and intersects the other two sides of the triangle, then those sides are divided proportionally.

directrix · Answer

OB is to BT as OA is to AU.

1.5/.5 = x / .45  where OA = x

x = 1.35

directrix · Answer

By the Segment Addition Postulate, GE = OE - OG = 5.8 - 4.35 = 1.45

directrix · Answer

Also, by the Segment Addition Postulate, OU = OA + AU = 1.35 + .45 = 1.8

directrix · Answer

That leaves TS and SE as still unknown.

milalulu · Answer

Makes so much more sense! thank you for your help!! @directrix

directrix · Answer

@milalulu 

We still need to work on these two:  That leaves TS and SE as still unknown.

wolf1728 · Answer

I figured I'd update my graphic with the recently-obtained dimensions.