Question

Please help!

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 1

is there a picture to go along with this ?

Answer 2

Yes! posting right now

Answer 3

i dont see the letter D

Answer 4

in the diagram

Answer 5

You don't need D?

Answer 6

D = triangle

Answer 7

Sorry about the confusion

Answer 8

It is a triangle symbol that has been mistranslated. There is no quadrilateral DTRI, just \(\Delta TRI\)

(it was a Delta)

Answer 9

oh

Answer 10

Capital Delta can be written in LATEX with \Delta, by the way, or in the equation editor.

Answer 11

Thanks @Valpey for clearing that up!

Answer 12

ok we can use the side splitter theorem

Answer 13

thanks for clarifying

Answer 14

The sidesplitter theorem tells us
$$
\Large \frac{TA}{AR}= \frac {TN}{NI}

$$

Answer 15

Okie!

Answer 16

lets step back for a moment, instead of writing down ratios.
we have two similar triangles, because of the two parallel lines

Answer 17

triangle TAN is similar to triangle TRI.
and corresponding sides are proportional

Answer 18

1. AN is parallel to RI (Given)
2. <TAN = <TRI (parallel lines form corresponding congruent angles)
3.