Early Math · Grades 1, 2

What Makes a Shape: Sides, Angles and Faces

Quick answer

A shape's name depends on its defining attributes: a triangle is closed and has three straight sides. Color, size and the way it is turned are not defining, so they never change the name. Counting sides or angles names the shape: 3 makes a triangle, 4 a quadrilateral, 5 a pentagon and 6 a hexagon, whether or not the sides are equal. A cube is a solid with 6 faces that are all equal squares.

What you'll learn

  • Tell defining attributes of a shape from attributes that do not define it
  • Name triangles, quadrilaterals, pentagons and hexagons by their sides and angles
  • Describe a cube by its faces, and draw shapes with given attributes

What makes a triangle a triangle

All of these are triangles.

All of these are triangles Four triangles: an orange one, a small blue one turned upside down, a long green one with a square corner, and a purple one leaning to the right.
All of these are triangles

They come in lots of colors and sizes. They face all ways. But each one is closed and has 3 straight sides. That is what makes a triangle.

These are not triangles:

Not triangles Three shapes that are not triangles: three sides with a gap so the shape is not closed, a circle, and a square. not closed no straight sides 4 sides
Not triangles

Why color and size do not matter

A shape’s name is a rule about its sides and corners. The rule for a triangle is: closed, with 33 straight sides.

Color is not in the rule. Size is not in the rule, and neither is the way the shape is turned. So none of them can change the name. The things in the rule are called defining attributes.

Name a shape by its sides

Count the straight sides. Each side ends at an angle. An angle is the corner where two sides meet. So you can count angles too.

Sides and anglesName
33triangle
44quadrilateral
55pentagon
66hexagon

The sides do not have to be the same length.

Shapes named by their sides Four shapes: a quadrilateral with no two sides equal, a pentagon shaped like a house, an L-shaped hexagon, and a regular hexagon. quadrilateral pentagon hexagon hexagon
Shapes named by their sides

Squares, rectangles, rhombuses and trapezoids all have 44 sides. So they are all quadrilaterals.

Faces of a cube

A cube is a solid shape. Its flat sides are called faces.

A cube has 66 faces. Every face is a square, and all 66 squares are the same size. It also has 88 corners and 1212 edges, where two faces meet.

Worked examples

Common mistakes

Practice problems

  1. Is this shape a triangle? Why or why not?

    Is it a triangle? Three straight sides with a gap between two of them, so the shape is not closed.
    Is it a triangle?
    Answer

    No. It is not closed.

    Full solution

    It has 33 straight sides, but there is a gap. A triangle must be closed.

  2. A shape has 66 straight sides. What is it called?

    Answer

    A hexagon

    Full solution

    66 sides makes a hexagon, whatever the side lengths are.

  3. How many angles does a pentagon have?

    Answer

    55

    Full solution

    A pentagon has 55 sides, and each side ends at an angle. So it has 55 angles.

  4. Name this shape.

    Name this shape A closed shape with four straight sides, none of them the same length.
    Name this shape
    Answer

    A quadrilateral

    Full solution

    Count the sides: 44. It is closed, and the sides are straight.

  5. What makes a square a square: its color, its size, or its 44 equal sides?

    Answer

    Its 44 equal sides

    Full solution

    A red square and a blue square are both squares, and so are big and small ones. Four equal sides and four square corners make a square.

  6. How many faces does a cube have? What shape is each face?

    Answer

    66 faces; each one is a square.

    Full solution

    Top, bottom, front, back, left and right: 66 faces, all equal squares.

  7. Is a rectangle a quadrilateral?

    Answer

    Yes

    Full solution

    A rectangle is closed and has 44 straight sides. So yes, it is one.

  8. Name this shape.

    Name this shape A closed shape shaped like a house: a square bottom with a pointed roof.
    Name this shape
    Answer

    A pentagon

    Full solution

    Count the sides: the bottom, two walls and two roof sides make 55.

  9. Draw a shape with 33 angles. What is it called?

    Answer

    A triangle

    Full solution

    Put three dots that are not in a line and join them. The closed shape has 33 sides and 33 angles.

  10. Ivy says a shape is not a hexagon because its 66 sides are not all the same length. What went wrong?

    Hint

    What is the rule for a hexagon?

    Answer

    Equal sides are not part of the rule. Closed, with 66 straight sides, is all it takes.

    Full solution

    The rule for a hexagon is: closed, with 66 straight sides.

    Side length is not in the rule. So the shape is a hexagon.

Frequently asked questions

What are the defining attributes of a triangle?

It is closed, and it has 3 straight sides and 3 angles. Color, size and how it is turned do not matter.

What is a quadrilateral?

Any closed shape with 4 straight sides. Squares, rectangles and trapezoids are all quadrilaterals.

Does a hexagon need 6 equal sides?

No. Any closed shape with 6 straight sides is a hexagon, even one shaped like the letter L.

What is an angle?

The corner where two sides of a shape meet. A shape with straight sides has as many angles as sides.

How many faces does a cube have?

6, and they are all squares of the same size. A cube also has 8 corners and 12 edges.

What to learn next

Standards alignment

This lesson covers the following Common Core State Standards for Mathematics.

  • CCSS.MATH.CONTENT.1.G.A.1GeometryDistinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
  • CCSS.MATH.CONTENT.2.G.A.1GeometryRecognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
For teachersTick to print a blank worksheet; leave it clear to print the lesson with the full answer key.