The 1st-house ruler is the planet that governs the sign rising at your birth. It describes what you arrive with: your instinct, your default move, the version of you that walks into the room before anyone has spoken. The 7th ruler describes the counterpart who keeps turning up. Put the two side by side and the chart starts separating your own material from what you keep meeting.
Start with the Ascendant. Suppose Libra rises and Venus rules it. Venus's sign and house show how you open, what you value, and the tone you bring without being asked. Now suppose Aries sits on your 7th cusp, ruled by Mars. Those two rulers — Venus and Mars — are your baseline comparison. Where they contact each other in the chart, the relationship between self and other has a built-in channel. Where they ignore each other, that gap is where misreading the other side becomes a habit.
The clearest projection signal is a 7th ruler making hard contact to the 1st ruler, or to the Ascendant itself. A square between them describes the traits you dislike in other people that you have not claimed in yourself. The colleague who is too blunt, the partner who never compromises, the rival who plays dirty: check whether the 7th ruler sits on a sign whose qualities your 1st ruler refuses to express. The opponent is telling you something about your own range.
The mutuality signal runs the other way. When the 1st ruler and 7th ruler sit in compatible signs, or form a sextile or trine, the exchange is genuine. You meet people as equals and the terms are negotiated rather than imposed. That is partnership in the functioning sense: two rulers in dialogue, not one ventriloquizing the other.
The comparison also answers the question readers actually ask. If your 1st ruler is strong and dignified while the 7th ruler sits weakly placed, your instinct may be to over-function and pick people who need managing. If the 7th ruler is strong and the 1st is under pressure, you may keep meeting counterparts who set the terms while you adapt. Neither pattern is a fate; both are readable, and both adjust once you see which ruler is doing the driving.
Run the test before your next negotiation. Open your saved chart, find the Ascendant sign and the 7th cusp sign, then list both ruling planets with their signs, houses, dignities and any contact between them. That short list is the honest comparison — projection on one side, real negotiation on the other.