The most extreme northern and southern parallels to experience perpendicular rays of the Sun at local noon are located at the Tropic of Cancer (23.5° N) and the Tropic of Capricorn (23.5° S).

Here's why:

* Earth's Tilt: The Earth is tilted on its axis at approximately 23.5 degrees. This tilt is responsible for the seasons.

* Solar Declination: The Sun's apparent position in the sky changes throughout the year, moving between 23.5° North and 23.5° South. This movement is known as the solar declination.

* Perpendicular Rays: When the Sun's rays hit a location directly overhead (at a 90-degree angle), it's called a solar zenith. This only happens twice a year at locations between the Tropics of Cancer and Capricorn.

* Maximum Reach: The Tropics of Cancer and Capricorn represent the furthest north and south that the Sun's declination reaches, meaning they are the most extreme parallels where the Sun's rays can be perpendicular at local noon.

Therefore, the Tropic of Cancer marks the northernmost point where the Sun can be directly overhead, and the Tropic of Capricorn marks the southernmost point.