Question

Reposting with higher point count AND the actual, like, chart.

My daughter needs help and I can't find this solution anywhere online to help her. Photo of tri is in photo. I spent 70 points on this, so I hope this gets answered.

For Triangle TOE, 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 for the following answers:

a. Why is triangle OBG ~ to triangle 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 side-splitting theorem.)

f. SE

g. OU


Her answers were:

a. AA similarity postulate (Unsure if correct but probably is, teacher didn't see answer.)

b. GE = 1.45 ("Fine?")

c. TS = 3 cm (INCORRECT)

d. OA = 1.35 cm (CORRECT)

e. BT = .5 cm (CORRECT)

f. SE = 3 cm (INCORRECT)

g. OU = 1.8 cm (CORRECT)

Answer 1

The answers to a, b, d, e, g are correct (as noted in your problem statement).

Explanation:

a) The triangles are similar because their apex angle is the same angle, and their base angles are corresponding angles where transversals cross parallel lines, hence congruent. The triangles are similar by AA (or AAA, if you like) since all corresponding angles are congruent.

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b) GE = OE -OG = 5.8 -435 = 1.45 . . . cm

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c) Technically speaking, there is not enough information in your posted question to allow TS to be found. You can find the length TU using the Pythagorean theorem. (First you need OU (see g below).) By that theorem, ...

TU^2 + OU^2 = OT^2

TU = √(OT^2 -OU^2) = √(2^2 -1.8^2) = √0.76 ≈ 0.87

By all appearances, US = TU. If you make that assumption, then ...

TS = 2·TU = 2·0.87 = 1.74 . . . cm

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d) We have seen that OG = 3·GE, so OA will be 3·AU.

OA = 3·AU = 3·0.45 = 1.35 . . . cm

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e) Using the same proportions we have observed elsewhere,

BT/OT = 1/4

BT = (2 cm)/4 = 0.5 cm

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f) SE = TE - TS = 6 cm - 1.74 cm = 4.26 cm

(see part (c) above for the assumption we must make regarding this)

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g) OU = OA + AU = 1.35 cm + 0.45 cm = 1.8 cm