Question

(please help fast medal given to best answer)
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:

Answer 1

@mathstudent55

Answer 2

@TheSmartOne

Answer 3

@nincompoop

Answer 4

Sorry, I don't remember how to do these very well.

Maybe @dan815 @jigglypuff314 @Michele_Laino could help you out? :D

Answer 5

@mathstudent55 can you help out

Answer 6

To prove two triangles are similar, one way is to prove two angles of one triangle are congruent to two corresponding angles of the other triangle.

Answer 7

Because of the two parallel segments, corresponding angles on each side are congruent.
Those are the two pairs of congruent corresponding angles.

Answer 8

The figure above shows two pairs of congruent corresponding anmgles.
That's enough to prove the triangles similar.

Answer 9

so that answers part a of the problem

Answer 10

Yes. You can write a two-column proof based on that. That would take care of part a.

Answer 11

There is an even quicker way to do part a.
All you need is one pair of angles from the parallel lines, and you can use angle T congruent to itself as the other pair of congruent angles.

Answer 12

Now let's look at part 2.
I'll fill in the given measures in the figure.