Question

1.For 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 TAN  TRI.
b)Assume TAN is the image of 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 TRI to TAN?

Answer 1

For the answer to the question above,
b.Triangle TAN being an image of triangle TRI is smaller than triangle TRI, and so is a contraction.
while,

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
I hope my answer helped you. Please ask one question at a time.