(feature discontinued) Google Hangouts phone app: How to start a group SMS where one of the recipients is a Hangouts user? I'm actually answering my own question here, and the purpose for this is because the question hasn't been clearly stated before.

Imagine the following scenario:


I have a friend named Joe who uses Google Hangouts on his cell phone
I have a friend named Mary who uses a cell phone, but does not have
Google Hangouts


I would like to send a group message to both of them.  I know that Joe can receive SMS or Hangouts, but Mary only has the capability to send/receive SMS/MMS.  How can I ensure my message is compatible for Mary?
You can do this in two different ways:

Method 1:


In Hangouts, tap the + button 
Tap "New SMS"
Find Mary and tap on her entry.  The combination of step 2 and 3 will solidify the message as an SMS.  If you select Joe (our Hangouts contact) first, it may convert to a Hangouts message, so it is important to start with your SMS contact first!  
Find Joe and tap on his entry
Tap the green arrow to continue.  In my case, I have two numbers I can send from (my carrier number or a Google Voice Number), so I would select my desired number.


Method 2:


In Hangouts, send a message to Mary
While staying in Mary's conversation, tap the "three dots" button in the upper right
Tap "New Group MMS"
Find Joe and tap on his entry
Tap the green arrow to continue.  In my case, I have two numbers I can send from (my carrier number or a Google Voice Number), so I would select my desired number.


Testing

In either situation, you can test if you were successful by tapping the "three dots" button in the upper right of your group message.


If the dropdown has an option for "Delete", then you are in a group SMS/MMS
If the dropdown has an option for "Leave", then you are in a hangout


Tested on Hangouts version 10.0