Yep, if it is painted, Titebond II or similar makes a joint as strong or stronger than the wood. CAREFULLY match the parts, apply glue with a small brush or force it into cracks, then use finish nails to hold the parts until dry. Sand edges smooth and paint. If stained, the repair will show, no matter how good you get the joints. Then is is best to replace, but that is not a simple job.
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