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Practicing the single leg bird dog variation is a helpful exercise drill to learn how to keep the core tight and engaged when extending a limb. It’s easier to focus on the keeping the core tight when just moving 1 leg as opposed to when you are moving both an arm and a leg from opposite sides in the standard bird dog exercise.
If you tend to arch and extend through your lower back when doing standard bird dogs this is a great drill to practice creating tension in your abs while extending a limb.