What are 2D Shapes?

2D shapes are flat shapes that have only two dimensions: length and width.

They have NO thickness or height - they are completely flat!

Important 2D Shape Vocabulary

• 📏 Sides (or Edges): The straight lines that form the shape
• 📍 Vertices (Corners): The points where two sides meet
• 🔺 Polygon: A closed 2D shape made of only straight lines

Important: One vertex, two or more vertices!

Key Formula for 2D Shapes

Number of Sides = Number of Vertices

(This rule works for all polygons!)

What are 3D Shapes?

3D shapes are solid shapes that have three dimensions: length, width, and height.

They are NOT flat - they have depth and take up space!

Important 3D Shape Vocabulary

• 🟦 Faces: The flat or curved surfaces of a 3D shape
• 📏 Edges: The line segments where two faces meet
• 📍 Vertices: The points (corners) where edges meet
• 🔶 Polyhedron: A 3D shape made of only flat faces

Euler's Formula for 3D Shapes

For any 3D shape made of flat faces (polyhedron), this special formula works:

\( V + F - E = 2 \)

Where: \( V \) = Vertices, \( F \) = Faces, \( E \) = Edges

This formula ALWAYS equals 2 for shapes with flat faces!

Comparing 2D Shapes

To compare 2D shapes, count and compare their:

• Number of sides
• Number of vertices (corners)
• Types of angles
• Side lengths (equal or different)

Example: A square has 4 equal sides and 4 vertices. A triangle has 3 sides and 3 vertices. The square has \(4 - 3 = 1\) more side than a triangle.

Comparing 3D Shapes

To compare 3D shapes, count and compare their:

• Number of faces
• Number of edges
• Number of vertices
• Type of faces (flat or curved)

Example: A cube has \(6\) faces and a cone has \(2\) faces. The cube has \(6 - 2 = 4\) more faces than the cone.

What are Transformations?

Transformations are different ways to move or change the position of a shape.

There are three main types of transformations: Slide, Flip, and Turn.

1️⃣ Slide (Translation)

A slide (or translation) moves a shape from one place to another in a straight line.

➡️ The shape moves but does NOT change size, direction, or orientation!

• The shape looks exactly the same, just in a new position
• Can slide up, down, left, right, or diagonally
• All points move the same distance and direction

Real-Life Examples: Sliding a book across a table, moving a car forward, pushing a toy

2️⃣ Flip (Reflection)

A flip (or reflection) creates a mirror image of a shape.

🪞 The shape is flipped over a line, like looking in a mirror!

• Horizontal Flip: Flip over a horizontal line (left and right switch)
• Vertical Flip: Flip over a vertical line (top and bottom switch)
• The shape faces the opposite direction after flipping

Real-Life Examples: Looking in a mirror, reflection in water, flipping a pancake

3️⃣ Turn (Rotation)

A turn (or rotation) spins a shape around a fixed point.

🔄 The shape rotates like a wheel turning around its center!

• Clockwise Turn: Turning in the same direction as clock hands ↻
• Counterclockwise Turn: Turning opposite to clock hands ↺
• Quarter Turn: Rotating \(90°\) (like turning a corner)
• Half Turn: Rotating \(180°\) (turning halfway around)

Real-Life Examples: Turning a doorknob, spinning a wheel, rotating a fan blade

For 2D Shapes (Polygons):

• ✓ Number of Sides = Number of Vertices
• ✓ Triangle: \(3\) sides, \(3\) vertices
• ✓ Quadrilateral: \(4\) sides, \(4\) vertices
• ✓ Pentagon: \(5\) sides, \(5\) vertices
• ✓ Hexagon: \(6\) sides, \(6\) vertices
• ✓ Octagon: \(8\) sides, \(8\) vertices
• ✓ Circle: \(0\) sides, \(0\) vertices (curved shape)

For 3D Shapes (Polyhedrons):

Euler's Formula: \( V + F - E = 2 \)

• ✓ Cube: \(6\) faces, \(12\) edges, \(8\) vertices
• ✓ Cuboid: \(6\) faces, \(12\) edges, \(8\) vertices
• ✓ Square Pyramid: \(5\) faces, \(8\) edges, \(5\) vertices
• ✓ Triangular Prism: \(5\) faces, \(9\) edges, \(6\) vertices
• ✓ Sphere: \(1\) face, \(0\) edges, \(0\) vertices
• ✓ Cylinder: \(3\) faces, \(2\) edges, \(0\) vertices
• ✓ Cone: \(2\) faces, \(1\) edge, \(1\) vertex

For Transformations:

• ✓ Slide (Translation): Shape moves but stays the same
• ✓ Flip (Reflection): Shape creates mirror image
• ✓ Turn (Rotation): Shape spins around a point
• ✓ Quarter Turn: \(90°\) rotation
• ✓ Half Turn: \(180°\) rotation
• ✓ Full Turn: \(360°\) rotation (back to start)