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.
Other angles are just smaller than a square corner (sharper) or bigger than one (wider). On the test you only need to spot the right angle.
4 · Lines: parallel, perpendicular, crossing
Parallel lines go the same way and never meet, however far you draw them, like the two rails of a train track.
Perpendicular lines meet in a right angle, like the corner of a window. Lines that cross without a square corner are just intersecting.
Look for these in shapes: a rectangle has 2 pairs of parallel sides, and its sides meet at perpendicular corners.
5 · 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.
6 · 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.
7 · 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.
8 · 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.
9 · Same size and shape
Two shapes match when they are exactly the same size and shape, even if one is turned or flipped. You could lay one right on top of the other.
10 · 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.
11 · 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.
12 · Nets: unfold a box
A net is a solid cut open and laid flat. A cube net has 6 squares, one for each face.
Not every 6 squares will fold into a cube. Picture folding: one square is the bottom, four fold up as the walls, and the last one closes the top. If two squares would land on the same face, or there is no square left to make the top, it is not a cube net.
13 · 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.
14 · Equal parts
A shape is cut into fourths only if the 4 parts are the same size. Four parts of different sizes are not fourths, even though there are four of them.
Before you name a fraction of a shape, check that the parts are equal. Then count: 1 shaded part out of 4 equal parts is one fourth.
15 · 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.
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