Introduction to Quadrilaterals

Geometry · Axiom Academy

Introduction to Quadrilaterals Four-sided polygons and their special properties If it has four straight sides, it's a quadrilateral A quadrilateral is any polygon with exactly four sides and four vertices. From tidy squares to strange, lopsided shapes, anything closed with four straight sides counts. They are everywhere — screens, windows, tabletops, road signs — and a single fact ties every one of them together. Here is the fact: the four interior angles of any quadrilateral always add to 360°. Watch why. Drawing one diagonal cuts the shape into two triangles — and the angles of each triangle add to 180°. Two triangles, 180° + 180° = 360° . The four corner angles always total 360° — no matter how stretched or skewed the quadrilateral is. Most quadrilaterals you'll meet have names, earned by extra structure — right angles, equal sides, or parallel sides. Here are the six that matter most. 4 right angles, opposite sides equal 4 right angles, all sides equal Opposite sides parallel and equal All sides equal, opposite angles equal Exactly one pair of parallel sides Two pairs of consecutive equal sides Every one of these still obeys the 360° rule — the names just add extra promises on top. Some of these shapes are really special cases of others. A square is a special rectangle, which is a special parallelogram — so a square inherits every property above it in the tree. Read it top-down: each shape below is a more specialized version of the one it hangs from.

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