Replacement pivot bar

We recently purchased a house and realized that none of the windows close completely, and several of the upper sashes won't stay up when not latched. On removing the sashes, we found that none had pivot bars although the frames have balance shoes in them. It's not clear whether all the bars broke at some point or were never installed. I attached a picture of the bottom of one of the top sashes where I believe the pivot bar would seat, and I wondered whether you could recommend a replacement part that would fit those dimensions so we could replace them all. Thank you.

After taking more of the window sashes down, we found one broken pivot bar, picture attached. From comparing it with bars on the site, I believe it's this one: https://www.swisco.com/Pivot-Bar-3-1_16-inch/pd/Tilt-Window-Replacement-Sash-Pivot-Bars/26-226

Does that look right? Is there any particular measurement we should do to confirm?