Diagonals of a Polygon Formula: Why It's ⁿC₂ − n (Full Logic Explained)

Ever wondered why the formula for the number of diagonals in a polygon is ⁿC₂ − n? In this clip, we break down the exact logic behind this important geometry formula — step by step, using a pentagon (5-sided polygon) as our working example. You'll see visually why simply taking every possible combination of two points (ⁿC₂) isn't enough to get the number of diagonals — and why we must subtract 'n' from it. We walk through exactly which point-pairs form diagonals (like AC, AD, BD, BE, CE in a pentagon) and which ones actually form sides instead (which get wrongly counted if you don't subtract n). Key points covered in this clip: What counts as a diagonal vs. a side in any polygon Why adjacent vertices never form a diagonal How every 2-point combination includes the polygon's sides too Why we subtract 'n' (the number of sides) from ⁿC₂ Why this formula works the same for regular AND irregular polygons Worked example: verifying the formula using a pentagon (5 diagonals) This is a must-watch for anyone confused about where the "−n" in the diagonal formula comes from — instead of just memorizing ⁿC₂ − n, you'll actually understand why it works. Perfect for students preparing for competitive exams, geometry chapters on polygons and quadrilaterals, and anyone who wants formulas to make logical sense rather than being rote-learned. Watch till the end for the complete step-by-step derivation!