1 · Sides and vertices
A polygon is a closed shape made of straight sides. Where two sides meet is a corner, called a vertex (more than one: vertices).
Count the sides to name it: triangle 3, quadrilateral 4, pentagon 5, hexagon 6, octagon 8. A polygon has the same number of vertices as sides.
2 · Not a polygon
A circle has no straight sides, so it is not a polygon. An open shape is not a polygon either: the sides must close up with no gap. Curvy sides do not count.
3 · Angles
An angle is the opening at a vertex. A right angle is a perfect square corner, like the corner of a book. We mark it with a tiny square.
Smaller than a right angle is acute (sharp). Bigger is obtuse (wide).
4 · Rectangles and squares
A rectangle has 4 right angles, and its opposite sides are equal. A square has 4 right angles and all 4 sides equal (the tick marks show equal sides).
So every square is also a rectangle. But a rectangle is only a square if all its sides match.
5 · The rest of the quadrilateral family
Any 4-sided shape is a quadrilateral. A rhombus has 4 equal sides but its corners can lean. A parallelogram has two pairs of parallel sides (the arrows), like a leaning rectangle. A trapezoid has just one pair of parallel sides.
Parallel sides run side by side and never meet, like train tracks.
6 · Kinds of triangles
Triangles get names from their sides: equilateral (all 3 equal), isosceles (2 equal), scalene (none equal).
A triangle with a square corner is a right triangle.
7 · Symmetry
A shape has a line of symmetry if you can fold it on that line and the two halves match exactly.
A rectangle has 2 lines of symmetry. A square has 4: two through the middles and two through the corners.
8 · Congruent: same size and shape
Two shapes are congruent if they are exactly the same size and shape, even if one is turned or flipped. You could lay one on top of the other.
9 · Solid shapes
Solids are 3D: they have height, width, and depth. The cube (a dice), the rectangular prism (a box), the sphere (a ball), the cylinder (a can), the cone (an ice-cream cone), and the pyramid.
10 · Faces, edges, vertices
A face is a flat side. An edge is where two faces meet. A vertex is a corner point.
A cube has 6 faces, 12 edges, 8 vertices. A rectangular prism has the same counts. A square pyramid has 5 faces (1 square + 4 triangles), 8 edges, 5 vertices. A sphere has no faces, edges, or vertices at all.
11 · Shapes inside shapes
Cut a rectangle corner to corner and you get 2 triangles. A hexagon can be split into 6 triangles from its center. Splitting into equal parts is how fractions begin.
12 · Sorting by the rules
Test questions describe a shape and ask you to name it. Go rule by rule: "4 sides" (quadrilateral), "opposite sides parallel" (parallelogram, rectangle, rhombus, or square), "no right angles" (parallelogram or rhombus), "all sides equal" → rhombus.
Check every rule, then cross off the shapes that break one. You are ready for the test! 🎉
Ready to check what stuck?
Take the free 24-question test. It starts easy and builds to harder, ISEE-style reasoning. It's auto-scored, and you can review every answer afterward.