This is a well known problem.

The tie notation may not be “theoretically” correct, but it is not uncommon, and the performers will understand.

You can get the ties, with some work:

1) On the first beat, enter a quarter note.

This note can be tied to the next beat.

2) Speedy Entry Tool.

Go back on the first beat (quarter note), and launch Voice 2 (= hit the ' key).

In the Speedy Entry rectangle, in the top left corner, you will see ‘V2’.

Enter the triplet in Voice 2.

You can tie the last triplet eighth to the following chord.

3) Now only the middle note remains.

You can enter that in another layer.

Hide the initial triplet eighth rest.

Enter the note as a triplet quarter (hide the triplet).

Enter a quarter note on the next beat.

You can tie the two notes together.

It may be necessary to flip some stems and some ties, but you can get the desired layout.

Below, I have simulated the ties with slurs. 

That looks fine. Why not just use it? I would think way better than going through all that work around especially if you have a lot of them.

If you have “a lot of them”, do only one measure, and copy that measure to the other measures.

Then, adjust the pitches with the Simple Entry Tool sub-tool Repitch Tool.

If you have never tried the Repitch Tool, then I recommend that you try it; it is really fast.

That looks fine. Why not just use it? I would think way better than going through all that work around especially if you have a lot of them.

Because with the "long" method, playback will be correct.

If you have “a lot of them”, do only one measure, and copy that measure to the other measures.

Then, adjust the pitches with the Simple Entry Tool sub-tool Repitch Tool.

Even so, even with all the 'extras' Finale has, it is more work depending on how many measures there is. There is no right or wrong way if what you end up with is what you want. Finale is so versatile it has many ways to accomplish and end. That's what makes it the best.

There is a name for that broken arpeggio chord, but damme if I can remember it, now. However, it’s been on the feature wish list for a decade, if not more.

Wow!

Thanks, everybody, for another spirited set of responses.

Last first--that term had escaped my brain, also. It is simply a "broken chord." There are scales, arpeggios, and "broken chords." ;-)

Next. I have never even heard of the "Repitch Tool." Really cool. I had simply (no pun intended) thought is was a double-double-whole-note... I will be using this a lot in the future.

Next, the slurs are what I have been using, and it looks acceptable. But for playback, the bottom two notes sound again. Usually--for playback--I add each note and tie to it as it unfolds, but that becomes cumbersome and does not look good.

Lastly, for some reason the V1 is vaguely visible on my screen, so I had never really seen them before.
Unfortunately, Peter, pressing the apostrophe ` key does not change V1 to V2.

If I can get that to work I will try your solution.

:-)
Nessa

… pressing the apostrophe ` key does not change V1 to V2 …

Vanessa,

I think that you are pressing the wrong key on the computer keyboard.

In your post you have pressed the accent (`) key.

The apostrophe (') key produces the vertical apostrophe symbol.

I do not know what keyboard layout you have selected in your operating system, but I suspect that you have the apostrophe (') key next to the Return key.

Quoting the manual:

“To enter Voice 2, press the apostrophe (') key.”

… It is simply a "broken chord." There are scales, arpeggios, and "broken chords." …

Somebody once called it a “pyramid chord”.

Not the “official” name for it, but you understand the meaning.

Thank you, Peter

Serves me right for burning post-midnight oil. Apostrophe is the key!

:-)
Nessa