Question

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:
a) In two-column format prove that triangle TAN ~ triangle TRI.
b) Assume triangle TAN is the image of triangle TRI 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 triangle TRI to triangle TAN?

Answer 1

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