Question

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Answer 1

Your link posted does not lead to the image. Can you re-post it or upload through the "Attach Files" button?

Answer 2

Yep, thanks. :)

Answer 3

So, at what part are you on right now that you needed help with?

Answer 4

Ah, I see.
So, starting with (a), I assume it is meant to ask, prove the two triangles are similar? (It seems like it was copied and pasted here, but some things got muddled in the transit)

Answer 5

Yep, got it. So there are a few ways to show triangles are similar. If I recall correctly (it has been a while since I had Geometry!), we could show the angles are the same or show that there is some ratio between the corresponding side lengths.

Answer 6

Sure, I like the angle idea too. And I can already see one angle in common!
Notice that triangles TAN and TRI both share the vertex T, so that angle is naturally the same between the two.

Answer 7

That can be one of the most easily overlooked to find.
So we just need one more pair of angles shown to be congruent. The parallel lines look like a red flag to me because there are a lot of theorems about a transversal splitting two parallel lines, right?

Answer 8

Just drawing it here to see it easily.

Answer 9

<T = <T This one is an identity.
The next part is one of those theorems. But I don't quite know which ones you learned. Does one along the lines of "corresponding angles of parallel lines cut by a transversal are congruent" sound familiar?

Answer 10

The specific theorem would then be the justification to show that either of these sets of angles are congruent:

You could do so for either or both that you like, because either way we would have shown by AAA similarity postulate that they are similar for the final statement.

Answer 11

Yep.
Remember when I said, similar triangles have a specific ratio of side lengths?
It came back to haunt us.

Answer 12

Do not fear, though, because we only need to divide two numbers!
They gave us a bunch of arbitrary side lengths here:
AN = 6 cm
RI = 8 cm
TA = 3.3 cm
NI = 1.6 cm

Answer 13

In the two triangles we showed being similar, you have sides that correspond to one another. You know what I mean by this?

Answer 14

Like, we have the sides TA and TR. They both share the angle T and that set of angles <R and <A which are congruent as well.

Answer 15

If we are given two corresponding sides' lengths in those four side lengths, we find the scale factor by dividing the larger by the smaller. Do you see any of those sides listed corresponding to one another?

Answer 16

TA was paired with TR