Welcome to the world of polygons! From triangles to hexagons, learn to identify, classify, and analyze 2D shapes by their sides, vertices, and angles. Geometry is everywhere! 🔷🔶🔸
Master polygon identification and properties!
Learn the defining properties of polygons!
Match polygons to their side counts!
🖱️ Drag options below to the correct boxes (computer) or click to move (mobile)
Identify special four-sided shapes!
Click on all the true polygons!
Click all correct options
Explore 7 essential polygon concepts!
A polygon is a special type of 2D shape! It must be CLOSED (no gaps - you could trace it without lifting your pencil), made entirely of STRAIGHT sides (no curves anywhere), and have at least 3 sides meeting at corners called vertices. 'Poly' means many, 'gon' means angles - so polygon literally means 'many angles!' The world is full of polygons!
Polygon = closed 2D shape made of straight line segments
Must have at least 3 sides (triangle is simplest)
Sides connect at vertices (corners/endpoints)
NO curves allowed (circles aren't polygons!)
Examples: triangles, squares, pentagons, hexagons, octagons
Quick polygon test: Is it closed? Are all sides straight? If YES to both, it's a polygon! If NO to either, it's not!
Thinking ANY closed shape is a polygon! Circles and ovals are closed but have curves, so they're NOT polygons. Straight sides are required!
Polygons are everywhere! Stop signs (octagon), floor tiles (squares, hexagons), buildings (rectangles), pizza slices (triangles), soccer ball patches (pentagons/hexagons)!
Polygon hunt! Walk around and find polygons in your environment. Photograph or draw them. Identify how many sides each has!
Triangles are the foundation of geometry! With just 3 sides, they're the simplest polygons. But don't let simplicity fool you - triangles are incredibly strong (that's why bridges and buildings use triangle structures!). Every triangle has 3 sides, 3 vertices, and 3 angles. Learning triangles helps you understand all other polygons!
Triangle = polygon with exactly 3 sides and 3 vertices
3 sides also means 3 angles (every vertex has an angle)
Types: equilateral (all sides equal), isosceles (2 equal), scalene (none equal)
Types by angles: right (has 90° angle), acute (all angles < 90°), obtuse (one angle > 90°)
Triangles are the simplest and strongest polygons!
Remember: sides = vertices = angles for ALL polygons! Triangle has 3 of each. Pentagon has 5 of each. The numbers always match!
Thinking triangles must 'point up' like △. Triangles can be rotated any direction and still be triangles! △ ▷ ▽ ◁ all triangles!
Pizza slices, road signs (yield), pyramids, roof trusses, sail boats, mountain shapes - triangles are everywhere in nature and design!
Draw 10 different triangles! Make some tall, some wide, some with a flat bottom, some tilted. See how varied triangles can be!
'Quad' means 4, so quadrilateral means 4-sided polygon! There are many special types with unique properties. Squares and rectangles are most common (windows, doors, books), but rhombuses, trapezoids, and parallelograms are also quadrilaterals. All quadrilaterals have 4 sides, 4 vertices, and 4 angles - but the side lengths and angle sizes vary!
Quadrilateral = any polygon with 4 sides and 4 vertices
Square: 4 equal sides, 4 right angles (90°)
Rectangle: opposite sides equal, 4 right angles
Rhombus: 4 equal sides, angles not necessarily 90°
Trapezoid: exactly 1 pair of parallel sides
Hierarchy: All squares ARE rectangles (4 right angles), but not all rectangles are squares! Understanding shape relationships helps classification!
Thinking quadrilaterals must look like squares/rectangles! Irregular 4-sided shapes (like kites or weird quadrilaterals) are still quadrilaterals!
Buildings (rectangular walls), computer screens, books, doors, windows, picture frames, tiles, flags - quadrilaterals dominate human design!
Quadrilateral sorting! Draw or cut out various 4-sided shapes. Sort into categories: squares, rectangles, rhombuses, trapezoids, other. Compare properties!
Pentagons step up the complexity with 5 sides! A regular pentagon (like the Pentagon building) has all equal sides and angles, looking balanced and symmetrical. Irregular pentagons have varying side lengths and angles but still have exactly 5 sides. 'Penta' means 5 in Greek, so pentagon = 5-sided shape. Less common than triangles/quadrilaterals but still important!
Pentagon = polygon with exactly 5 sides and 5 vertices
Regular pentagon: all 5 sides equal, all 5 angles equal
Irregular pentagon: sides/angles differ in size
The Pentagon building in Washington D.C. is a famous pentagon!
Pentagons appear in nature: some flowers, starfish have 5-fold symmetry
Pentagon = 5 everything! 5 sides, 5 vertices, 5 angles. Count any one and you know them all!
Drawing pentagons with only 4 or 6 sides! Count carefully. Pentagon MUST have exactly 5 straight sides meeting at 5 vertices!
Home plate in baseball, some buildings, tiles in certain patterns, flowers with 5 petals, design elements, military symbols (Pentagon building)!
Challenge: Draw a regular pentagon (try to make all sides equal) without tools! It's tricky. Then use a ruler/compass and see the difference!
Hexagons are nature's favorite shape! Bees build hexagonal honeycomb because hexagons use less wax and are super strong. Regular hexagons have all equal sides and angles (each interior angle = 120°). They tessellate beautifully - fit together perfectly like floor tiles. 'Hexa' means 6, so hexagon = 6-sided polygon. Hexagons are everywhere once you start looking!
Hexagon = polygon with exactly 6 sides and 6 vertices
Regular hexagon: all 6 sides equal, all 6 angles equal (120° each)
Hexagons tessellate perfectly (fit together with no gaps)
Honeycomb cells are hexagons - efficient and strong!
Nuts and bolts often have hexagonal shapes
Look at honeycomb (real or pictures) - perfect hexagons! Nature is an amazing mathematician, choosing hexagons for strength and efficiency!
Confusing hexagons with pentagons or octagons! Count carefully: 6 sides = hexagon, 5 = pentagon, 8 = octagon. The prefix tells you!
Honeycomb, floor tiles, nuts (on bolts), pencil cross-sections, board game tiles (hex grids), architectural design, soccer ball patches!
Tessellation art! Draw many hexagons fitting together (no gaps or overlaps). Color them in patterns. Explore mathematical art!
Every polygon has three key features: sides (the straight edges), vertices (the corners/points), and angles (the space between sides at corners). Here's the magic: these three numbers are ALWAYS equal! A hexagon has 6 sides, 6 vertices, AND 6 angles. Knowing this relationship helps you quickly identify and describe any polygon!
Side = straight line segment forming part of the polygon
Vertex (vertices plural) = corner where 2 sides meet
Angle = space between two sides at a vertex
For ANY polygon: # sides = # vertices = # angles
Counting any one tells you all three!
Just count sides! Once you know side count, you automatically know vertex and angle counts (they're the same number). One count gives you three facts!
Mixing up vertices and angles! A vertex is a POINT (corner). An angle is the SPACE between two sides at that point. Different concepts at the same location!
Describing shapes ('This polygon has 7 sides, so it has 7 vertices and 7 angles'), classifying shapes, solving geometry problems!
Make a polygon chart! Draw polygons from 3 to 8 sides. For each, count and record sides, vertices, angles. See the pattern!
Polygon names come from Greek and Latin number prefixes! Learn the prefixes and you can name any polygon. Tri = 3, quad = 4, penta = 5, hexa = 6, hepta = 7, octa = 8, nona = 9, deca = 10. The suffix '-gon' means angle. So 'hexagon' literally means '6 angles' (which also means 6 sides!). These names are used worldwide!
3 sides = Triangle (tri = 3)
4 sides = Quadrilateral (quad = 4)
5 sides = Pentagon (penta = 5)
6 sides = Hexagon (hexa = 6)
8 sides = Octagon (octa = 8), 10 sides = Decagon (deca = 10)
Memorize common prefixes (3-10)! Once you know them, you can name polygons instantly just by counting sides. It's like a secret code!
Making up names! 'Six-sided shape' is okay informally, but the proper mathematical name is 'hexagon.' Learning correct terms builds mathematical literacy!
Math class, geometry, architecture, design, engineering - proper polygon names are universal mathematical language spoken everywhere!
Flashcards! Draw polygons on one side, write names on the other. Quiz yourself until naming becomes automatic. Master 3-10 sides!