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# What Are The Properties Of Shapes? Explained For Teachers, Parents And Kids

Here we provide a summary of the 2D shapes and 3D shapes covered at elementary and middle school with a specific focus on the properties of shapes that teachers and parents can support children to learn and understand.

For a more in-depth look at shapes, then the following articles are recommended: 2D Shape Check for Understanding Quiz Download Free Now!

### What are the properties of 2D shapes?

2D shapes have two dimensions, such as width and height. We will go into more detail classifying these below.

### What are the properties of 3D shapes?

3D shapes have three dimensions, such as width, height and depth. We will go into more detail classifying these below.

### When will children learn about the properties of 2D and 3D shapes?

Here’s what children will be taught about the properties of shapes through each grade level:

Schools following Common Core:

Kindergarten children should be able to:

• Recognize the difference between 2D (“flat”) and 3D shapes (“solid”) and name common 2D and 3D shapes, including: 2D shapes [for example, rectangles (including squares), circles and triangles]; 3D shapes [for example, cuboids (including cubes), pyramids and spheres].
• Compare 2D and 3D shapes to describe how they are the same and different, their parts (corners, sides) and other attributes (having sides that are equal).
• Model and/or draw shapes in the world, and compose simple shapes to form larger shapes.

#### 2D shapes in 1st Grade

1st grade students should be able to:

• Distinguish between defining attributes (ex: triangles are closed and three-sided) versus non-defining attributes (ex: color, orientation, size).
• Compose 2D (rectangles, squares, trapezoids, triangles, half-circles and quarter-circles) and 3D shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders)
• Use shapes to create a composite shape, and compose new shapes from the composite shape

#### 2D shapes in 2nd Grade

2nd grade students should be able to:

• Draw and recognize shapes having specified attributes (ex: a given number of angles, or a given number of faces).Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

#### 2D shapes in 3rd Grade

3rd grade students should be able to:

• Understand that shapes in different categories may share attributes (ex: a rhombus and a rectangle has the same number of sides)
• Shared attributes can define a larger categories (ex: quadrilaterals)
• Recognize rhombuses, rectangles, and squares as examples of quadrilaterals and be able to draw these quadrilaterals, as well as other quadrilaterals that do not fit these categories.

#### 2D shapes in 4th Grade

4th grade students should be able to:

• Identify points, lines, line segments, rays, and angles and perpendicular and parallel lines in 2D shapes.
• Classify 2D figures based on the presence or absence of parallel or perpendicular lines and angles of a specified size.
• Recognize and identify right triangles as a category.
• Recognize a line of symmetry for a 2D figure and be able to draw these

#### 2D shapes in 5th grade

5th grade students should be able to:

• Classify 2D figures in a hierarchy based on properties.
• Understand that attributes belonging to a category of 2D figures also belong to all subcategories of that category. (Ex: all rectangles have 4 right angles and squares are rectangles, so all squares have four right angles).

#### Other schools:

Based on your child’s state and school curriculum, they may be introduced to topics in a different order or in different grade levels. For example, if your child’s school follows the TEKS, your child will be introduced to shapes with 11- and 12-sides in the 2nd grade.

Below are some of the shapes children will need to know, including their properties, such as the number of sides.

### Properties of 2D shapes

#### Circles

• A semicircle has 2 sides; 1 curved side and 1 straight side. The full arc is a 180° angle.

#### Triangles (3-sided shapes)

• An equilateral triangle is a regular triangle and each angle equals 60°.
• A right-angled triangle (or right triangle) is any triangle with one right angle.
• A scalene triangle is an irregular triangle. All sides and angles are different.
• An isosceles triangle has two sides and two angles that are the same.

• A square is a regular quadrilateral and each angle equals 90°.
• A kite has two pairs of equal-length sides and the diagonals cross at right-angles.
• A rectangle has two pairs of parallel straight lines and each angle equals 90°.
• A rhombus has two pairs of parallel lines, as well as equal sides and opposite equal angles.
• A trapezoid has exactly one pair of parallel lines.
• A parallelogram has two pairs of parallel lines and opposite equal angles.

#### Polygons

• A pentagon is any shape with 5 sides. The interior angles add up to 540°.
• A hexagon is any shape with 6 sides. The interior angles add up to 720°.
• A heptagon or septagon is any shape with 7 sides. The interior angles add up to 900°.
• An octagon is any shape with 8 sides. The interior angles add up to 1080°.
• A nonagon is any shape with 9 sides. The interior angles add up to 1260°.
• A decagon is any shape with 10 sides. The interior angles add up to 1440°.

### Properties of 3D shapes

• A sphere has 1 curved surface.
• A hemisphere has 1 face, 1 curved surface and 1 edge.
• A cone has 1 face, 1 curved surface, 1 edge and 1 vertex.
• A tetrahedron, or triangular-based pyramid, has 4 faces, 6 edges and 4 vertices.
• A square-based pyramid has 5 faces, 8 edges and 5 vertices.
• A cylinder has 2 faces, 1 curved surface and 2 edges.

#### Prisms

• A triangular prism has 5 faces, 9 edges and 6 vertices.
• A cube has 6 faces, 12 edges and 8 vertices.
• A cuboid has 6 faces, 12 edges and 8 vertices.
• A pentagonal prism has 7 faces, 15 edges and 10 vertices.
• A hexagonal prism has 8 faces, 18 edges and 12 vertices.

### Properties of shapes questions

Put your children’s problem-solving skills to the test!

1. Which of these shapes is a pentagon?

2. Which shape has exactly 5 faces?

3. These two shaded triangles are each inside a regular hexagon. In each hexagon, is the triangle an equilateral, isosceles or scalene?

(Answer: 1st = isosceles / 2nd = scalene)

4. Here is a drawing of a 3D shape.

Complete the table.

(Answer: Faces = 6 / Vertices = 8 / Edges = 12)

5.  Is this rhombus a regular quadrilateral? Explain how you know.

(Answer: No – not all angles are the same)

Wondering about how to explain other key math vocabulary to your children? Check out our Math Dictionary For Kids And Parents.

You can also check out our similar blogs:

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The content in this article was originally written by primary school teacher Sophie Bartlett and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza. ##### Sophie Bartlett
Year 6 Teacher
Sophie teaches mixed age classes at a small school in central England. She is a self confessed grammar pedant and number nerd so we've welcomed her as a regular author and editor for Third Space Learning.
x #### 2D Shape Check for Understanding Quiz 