What is a similarity between the first- quarter moom and the third -quarter moom

A similarity between the first-quarter moon and the third-quarter moon is that they both occur exactly halfway through their respective phases.

In the first-quarter moon, half of the moon's visible surface is illuminated by sunlight, while the other half is in shadow. This phase occurs approximately one week after the new moon.

In the third-quarter moon, again, half of the moon's visible surface is illuminated by sunlight, while the other half is in shadow. This phase occurs approximately one week after the full moon.

So, both the first-quarter moon and the third-quarter moon mark the halfway point between the new moon and the full moon phases.