Introduction to Triangles

Geometry · Axiom Academy

Three sides, three angles, and a handful of rules that hold for every triangle there is. The one rule every triangle obeys A triangle is the simplest closed shape there is: three straight sides, three corners. That simplicity hides something powerful — a triangle's three angles are not free to be anything. Pin down a couple and the last one is forced. You don't have to take that on faith: watch the three corners come together. Watch the three corner angles tear off the triangle and swing down to meet at one point on the line. They tile together with no gap and no overlap — a perfectly straight angle. The running total climbs to exactly 180° . The three angles of any triangle always add up to a straight line — 180°. Drag the top corner anywhere you like. Triangles get one name from their sides (equal sides or not) and another from their biggest angle . Watch both names — and the side lengths and angles driving them — update as you move the corner. By sides: all three equal → equilateral ; exactly two equal → isosceles ; all different → scalene . By angles: biggest angle under 90° → acute ; exactly 90° → right ; over 90° → obtuse . Six kinds of triangle — and every one of them is somewhere under your fingertip. Not just any three lengths make a triangle

This is the written version of the interactive lesson above. See the full Geometry course.