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  1. For triangle TRI, 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:

AIn two-column format prove that triangle TAN ~ triangle TRI.
BAssume triangle TAN is the image of triangle TRI under a dilation. Is the dilation an expansion or a contraction? What is the scale factor?
CCalculate AR. Show your work.
DUse the Side-Splitting Theorem to find TN.
EWhat is the ratio of the area of triangle TRI to triangle TAN?

For triangle TRI, 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 f class=

Verified Answer :

nobillionaireNobley

b.) Triangle TAN being an image of triangle TRI is smaller than triangle TRI, and so is a contraction.

c.) TA/AN = TR/RI
3.3/6 = (3.3 + AR)/8
6(3.3 + AR) = 8 * 3.3 = 26.4
3.3 + AR = 26.4/6 = 4.4
AR = 4.4 - 3.3 = 1.1
AR = 1.1

d.)  TA/TN = TR/TI
3.3/TN = (3.3 + 1.1)/(TN + 1.6)
3.3(TN + 1.6) = 4.4TN
3.3TN + 5.28 = 4.4TN
4.4TN - 3.3TN = 5.28
1.1TN = 5.28
TN = 5.28/1.1 = 4.8
TN = 4.8

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