Unit Test, Part 2

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Date:

Graded Assignment

Unit Test, Part 2

Answer the questions below. When you are finished, submit this test to your teacher by the due date for full credit.

(20 points)

Score

1.     For DTRI, the following facts are given:

Segment AN || Segment RI

AN = 6 cm

RI = 8 cm

TA = 3.3 cm

NI = 1.6 cm

Use any or all of these facts to answer the following:

a)     In two-column format prove that DTAN ~ DTRI.

b)    Assume DTAN is the image of DTRI under a dilation. Is the dilation an expansion or a contraction? What is the scale factor?

c)     Calculate AR. Show your work.

d)    Use the Side-Splitting Theorem to find TN.

e)     What is the ratio of the area of DTRI to DTAN?

Answer:

(12 points)

Score

2.     The height of one solid limestone square pyramid is 24 m. A similar solid limestone square pyramid has a height of 30 m. The volume of the larger pyramid is 16,000 m³. Determine each of the following, showing all your work and reasoning.

a)     The scale factor of the smaller pyramid to the larger pyramid in simplest form.

b)    The ratio of the area of the base of the smaller pyramid to the larger pyramid.

c)     Ratio of the volume of the smaller pyramid to the larger.

d)    The volume of the smaller pyramid.

Answer:

(17 points)

Score

3.     For DTOE the following facts are given:

mÐTOS = mÐSOE

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 DOBG ~ DOTE?

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

Answer:

Your Score

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