Question

check my answers please:
3. For TOE the following facts are given:
mTOS = mSOE
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:
a) Why is OBG  OTE?
Now find the following missing lengths. Show all work or reasoning. Round non-integral lengths to the nearest hundredth.
b) GE
c) TS
d) OA
e) BT (Use the Side-Splitting Theorem.)
f) SE
g) OU

will put answers in the answers below :D

Answer 1

A) First note that both triangles OBG and OTE have the same common angle at vertex O. Therefore, the measure of angle BOG = the measure of angle TOE. Because OS bisects both angles BOG and TOE, it divides TS and SE into the same ratio as OT and OE. Furthermore, because BG is parallel to TE, OS also divides BG = BN + NG into the same ratio. That implies that the sides of the angle BOG are in the same ratio as the sides of angle TOE. Since OB in triangle OBG corresponds to OT in triangle OTE, and OG in triangle OBG corresponds to OE in triangle OTE, then triangles OBG and OTE are similar by equal ratios of corresponding parts.
B) GE = OE - OG
GE = 5.8 cm - 4.35 cm
GE = 1.45 cm
C) TS/SE = OT/OE
TS = SE (OT/OE)

Let TS = x and SE = 6 - x. (Recall that TE = 6.)
x = (6 - x)(2/5.8)
x = (6 - x)(0.344)
x = 6 (0.344) - 0.344x
x = 2.064 - 0.344x
x + 0.344x = 2.064
1.344x = 2.064
x = 2.064/1.344
x = 1.54 to the nearest hundredth
Since TS = x, then TS = 1.54 cm.
D) OA/OU = OG/OE
OA = OU (OG/OE)
OA = (OA + AU)(OG/OE)
OA = (OA + 0.45)(4.35/5.8)
OA = (OA + 0.45)(0.75)
OA = (0.75)OA + 0.3375
OA - (0.75) OA = 0.3375
(0.25)OA = 0.3375
OA = 0.3375/0.25
OA = 1.35 cm
E) BT = OT - OB
BT = 2 - OB
OB/OT = OA/OU
OB = OT(OA/OU)
OB = 2 [1.35/(1.35 + 0.45)]
OB = 2 (0.75)
OB = 1.50
Now plug OB = 1.50 into the equation BT = 2 - OB.
BT = 2 - OB
BT = 2 - 1.50
BT = 0.50 cm
F) SE = TE - TS
SE = 6 - 1.54
SE = 4.46 cm
G) OU = OA + AU
OU = 1.35 + 0.45
OU = 1.80 cm

Answer 2

i really need someone to go threw and check the math, i don't know how to put the picture of the triangle given

Answer 3

What does the square symbol here mean: For TOE.

Click on the blue DRAW button below and sketch the triangles or whatever figures are in the diagram. There is no way to do a Geometry proof without a figure.

Answer 4

@lilithmilligan Seriously need a diagram here.

Answer 5

try this

Answer 6

@Directrix yeah that should help

Answer 7

@lilithmilligan
The work that some yahoo did over at the Yahoo site is not something I care to check.

From the diagram:

a) Why is Triangle OBG congruent to Triangle OTE?

Line BG is given to be parallel to Line TE.
Therefore, <OBG is congruent to < OTE by the postulate that if two parallel lines are cut by a transversal, then correspoinding angles are congruent.

<BOG is congruent to <TOE by the Reflexive Property of Congruence.

Triangle OBG congruent to Triangle OTE by the AA Triangle Similarity Postulate.

Answer 8

OE is given to be 5.8.
OG is given to be 4.35.
By the Segment Addition Postulate,
GE = 5.8 - 4.35 = ?

@lilithmilligan

You can crank this out.

When you return to the OS site, we will work together on parts c-g.