I’ve attached a 20 second video.
My issue with the solution I’ve presented, is that I have to go back and delete individual lines to combine the faces.
If you make solid objects you could use Outer Shell to combine them.
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Also, unless you need the final product to be a Solid, it is often advantageous to create symmetrical objects as collections of a single component and leave them that way. Separate components can be mirrored or flipped to make the whole, the pieces can be merged visually by selecting and hiding any edges where the components touch. Depending on the use, keeping assemblies as collections of joined component instances can make adjusting the geometry much quicker and easier.
I would use the Curic Mirror plugin. I would leave the components separate and hide the intersection line
Nice suggestion but not for this situation since the OP is using SketchUp Free (web) which doesn’t allow the use of extensions.
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Oops, sorry!! I did not pay attention