This will be true even when the Moon is at perigee, and the Earth at aphelion.
From the en.wikipedia.org
It also moves noticeably faster across the sky because it moves fastest at perigee.
From the usatoday.com
With this Chandrayaan-1's apogee was raised to 37,900 km, and its perigee to 305 km.
From the en.wikipedia.org
So in each orbit, the moon reaches this closest point to us, called perigee.
From the stltoday.com
At its low point, or perigee, the capsule was at an altitude of 100 miles.
From the washingtonpost.com
With this its apogee was raised to 164,600 km, and the perigee to 348 km.
From the en.wikipedia.org
The last burn came during the third orbit when the perigee was lowered to 72 kilometers.
From the en.wikipedia.org
The GSOs will be in orbits with a 24,000 km apogee and 250 km perigee inclined at 29 degrees.
From the en.wikipedia.org
An argument of perigee of 270 degrees places apogee at the northernmost point of the orbit.
From the en.wikipedia.org
More examples
Periapsis in Earth orbit; the point in its orbit where a satellite is nearest to the Earth
An apsis (Greek: u1F01u03C8u03AFu03C2; plural apsides /u02C8u00E6psu1D7Bdiu02D0z/, Greek: u1F01u03C8u03AFu03B4u03B5u03C2) is an extreme point in an object's orbit. The word comes via Latin from Greek and is cognate with apse...
The position in a geocentric orbit at which the orbiting object is at its least distance from Earth.
Minimal distance between the Earth and the Sun on the Earth elliptical orbit around the Sun.
The innermost point of a terrestrial orbit
The closest point to Earth of any object orbiting Earth. The word periapsis is used for objects orbiting other planets.
Perigee is the minimum altitude above the Earth's surface attained during the spacecraft's orbit. Its value is input to the CREME software in either km or nautical miles.
The place in a planet's orbit which is nearest to the Earth. See Apogee.
The time of the month when the Moon is closest to the Earth. For further details of past and future Perigees please turn to the following link: Apogee/Perigee